pax_global_header00006660000000000000000000000064150277305770014527gustar00rootroot0000000000000052 comment=c7f6c2c3ff144b46d4674a4903444f1485144003 bim-1.1.8/000077500000000000000000000000001502773057700123055ustar00rootroot00000000000000bim-1.1.8/.hgignore000066400000000000000000000014231502773057700141100ustar00rootroot00000000000000syntax: regexp # The recurrent (^|/) idiom in the regexps below should be understood # to mean "at any directory" while the ^ idiom means "from the # project's top-level directory". (^|/).*\.dvi$ (^|/).*\.pdf$ (^|/).*\.o$ (^|/).*\.oct$ (^|/).*\.octlink$ (^|/)octave-core$ (^|/)octave-workspace$ (^|/).*\.tar\.gz$ ## Our Makefile target ^target/ ## Files generated automatically by autoconf and the configure script ^src/aclocal\.m4$ ^src/configure$ ^src/autom4te\.cache($|/) ^src/config\.log$ ^src/config\.status$ ^src/Makefile$ ^src/.*\.m$ # e.g. doc/faq/OctaveFAQ.info # doc/interpreter/octave.info-4 ^doc/.*\.info(-\d)?$ ^doc/\w*/stamp-vti$ ^doc/\w*/version\.texi$ # Emacs tools create these (^|/)TAGS$ (^|/)semantic.cache$ # Other text editors often create these (^|/)~.* bim-1.1.8/COPYING000066400000000000000000000430771502773057700133530ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 2, June 1991 Copyright (C) 1989, 1991 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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If the program is interactive, make it output a short notice like this when it starts in an interactive mode: Gnomovision version 69, Copyright (C) year name of author Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than `show w' and `show c'; they could even be mouse-clicks or menu items--whatever suits your program. You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the program `Gnomovision' (which makes passes at compilers) written by James Hacker. , 1 April 1989 Ty Coon, President of Vice This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License. bim-1.1.8/DESCRIPTION000066400000000000000000000006531502773057700140170ustar00rootroot00000000000000Name: bim Version: 1.1.8 Date: 2025-06-28 Author: Carlo de Falco, and others Maintainer: Carlo de Falco Title: PDE Solver using a Finite Element/Finite Volume approach Description: Package for solving Diffusion Advection Reaction (DAR) Partial Differential Equations Depends: octave (>= 3.8.0), fpl, msh Url: https://github.com/carlodefalco/bim Autoload: no License: GPLv2+ Tracker: https://github.com/carlodefalco/bim/issues bim-1.1.8/INDEX000066400000000000000000000022661502773057700131050ustar00rootroot00000000000000BIM >> BIM - Diffusion Advection Reaction PDE Solver Matrix assembly bim1a_advection_diffusion bim1a_advection_upwind bim1a_axisymmetric_advection_diffusion bim1a_axisymmetric_advection_upwind bim2a_advection_diffusion bim2a_advection_upwind bim2a_axisymmetric_advection_diffusion bim2a_axisymmetric_advection_upwind bim3a_advection_diffusion bim3a_osc_advection_diffusion bim1a_laplacian bim1a_axisymmetric_laplacian bim2a_laplacian bim2a_axisymmetric_laplacian bim3a_laplacian bim3a_osc_laplacian bim1a_reaction bim1a_axisymmetric_reaction bim2a_reaction bim2a_axisymmetric_reaction bim3a_reaction bim1a_rhs bim1a_axisymmetric_rhs bim2a_rhs bim2a_axisymmetric_rhs bim3a_rhs bim2a_boundary_mass bim2a_axisymmetric_boundary_mass bim3a_boundary_mass Pre-processing and Post-processing computations bim2c_mesh_properties bim3c_mesh_properties bim2c_unknowns_on_side bim3c_unknowns_on_faces bim2c_pde_gradient bim3c_pde_gradient bim2c_global_flux bim3c_global_flux bim1c_elem_to_nodes bim2c_tri_to_nodes bim3c_tri_to_nodes bim2c_intrp bim3c_intrp bim1c_norm bim2c_norm bim3c_norm Utilities bimu_bernoulli bimu_logm bim-1.1.8/NEWS000066400000000000000000000036431502773057700130120ustar00rootroot00000000000000Summary of important user-visible changes for bim 1.1.6: ------------------------------------------------------------------- ** Avoid complex conjugate when changing array shape in bim2a_reaction and bim2a_rhs. Summary of important user-visible changes for bim 1.1.5: ------------------------------------------------------------------- ** Improvement of the functions for stiffness matrix assembly in 2D axisymmetric configuration. Summary of important user-visible changes for bim 1.1.4: ------------------------------------------------------------------- ** Added new functions for cylindrical coordinates in axisymmetric configuration. ** Fixed some bugs in 1d upwind discretization. Summary of important user-visible changes for bim 1.1.3: ------------------------------------------------------------------- ** Added new projection functions. ** A function for the generation of 3D boundary matrices has been added that can be used in the implementation of Robin boundary condition and interface conditions. ** Added a set of functions for the computation of inf, L2 and H1 norms of piecewise constant and elementwise constant functions. Summary of important user-visible changes for bim 1.1.2: ------------------------------------------------------------------- ** Fixed a bug in 1d upwind discretization. ** Added function to compute gradient of a 3d scalar field. Summary of important user-visible changes for bim 1.1.1: ------------------------------------------------------------------- ** Added new functions to perform interpolation at arbitrary nodes. Summary of important user-visible changes for bim 1.1.0: ------------------------------------------------------------------- ** Added new functions implementing the Orthogonal Subdomain Collocation method in 3D. ** More functions for 3d problems were added. ** Demostrations of how to use the package are now in the wiki. bim-1.1.8/README000077700000000000000000000000001502773057700146662DESCRIPTIONustar00rootroot00000000000000bim-1.1.8/doc/000077500000000000000000000000001502773057700130525ustar00rootroot00000000000000bim-1.1.8/doc/fiume.geo000066400000000000000000000011061502773057700146510ustar00rootroot00000000000000Point (1) = {0, 0, 0, 0.1}; Point (2) = {1, 1, 0, 0.1}; Point (3) = {1, 0.9, 0, 0.1}; Point (4) = {0, 0.1, 0, 0.1}; Point (5) = {0.3,0.1,-0,0.1}; Point (6) = {0.4,0.4,-0,0.1}; Point (7) = {0.5,0.6,0,0.1}; Point (8) = {0.6,0.9,0,0.1}; Point (9) = {0.8,0.8,0,0.1}; Point (10) = {0.2,0.2,-0,0.1}; Point (11) = {0.3,0.5,0,0.1}; Point (12) = {0.4,0.7,0,0.1}; Point (13) = {0.5,1,0,0.1}; Point (14) = {0.8,0.9,0,0.1}; Line (1) = {3, 2}; Line (2) = {4, 1}; CatmullRom(3) = {1,5,6,7,8,9,3}; CatmullRom(4) = {4,10,11,12,13,14,2}; Line Loop(15) = {3,1,-4,2}; Plane Surface(16) = {15}; bim-1.1.8/doc/tutorial.html000066400000000000000000000060361502773057700156100ustar00rootroot00000000000000

This is a short example on how to use bim to solve a DAR problem.
The data for this example can be found in the doc directory inside the bim installation directory.

Create the mesh and precompute the mesh properties
The geometry of the domain was created using gmsh and is stored in the file fiume.geo 

[mesh] = msh2m_gmsh("fiume","scale",1,"clscale",.1);
[mesh] = bim2c_mesh_properties(mesh);

Construct an initial guess
For a linear problem only the values at boundary nodes are actually relevant

xu     = mesh.p(1,:).';
yu     = mesh.p(2,:).';
nelems = columns(mesh.t);
nnodes = columns(mesh.p);
uin    = 3*xu;

Set the coefficients for the problem: -div ( \alpha \gamma ( \eta \nabla u - \beta u ) )+ \delta \zeta u = f g

epsilon = .1;
alfa    = ones(nelems,1);
gamma   = ones(nnodes,1);
eta     = epsilon*ones(nnodes,1);
beta    = xu+yu;
delta   = ones(nelems,1);
zeta    = ones(nnodes,1);
f       = ones(nelems,1);
g       = ones(nnodes,1);

Construct the discretized operators
AdvDiff = bim2a_advection_diffusion(mesh,alfa,gamma,eta,beta);
Mass    = bim2a_reaction(mesh,delta,zeta);
b       = bim2a_rhs(mesh,f,g);
A       = AdvDiff + Mass;

To Apply Boundary Conditions, partition LHS and RHS
The tags of the sides are assigned by gmsh 

Dlist = bim2c_unknowns_on_side(mesh, [8 18]); 	   ## DIRICHLET NODES LIST
Nlist = bim2c_unknowns_on_side(mesh, [23 24]); 	   ## NEUMANN NODES LIST
Nlist = setdiff(Nlist,Dlist);
Fn    = zeros(length(Nlist),1);           	   ## PRESCRIBED NEUMANN FLUXES
Ilist = setdiff(1:length(uin),union(Dlist,Nlist)); ## INTERNAL NODES LIST


Add = A(Dlist,Dlist);
Adn = A(Dlist,Nlist); ## shoud be all zeros hopefully!!
Adi = A(Dlist,Ilist); 

And = A(Nlist,Dlist); ## shoud be all zeros hopefully!!
Ann = A(Nlist,Nlist);
Ani = A(Nlist,Ilist); 

Aid = A(Ilist,Dlist);
Ain = A(Ilist,Nlist); 
Aii = A(Ilist,Ilist); 

bd = b(Dlist);
bn = b(Nlist); 
bi = b(Ilist); 

ud = uin(Dlist);
un = uin(Nlist); 
ui = uin(Ilist);

Solve for the displacements

temp = [Ann Ani ; Ain Aii ] \ [ Fn+bn-And*ud ; bi-Aid*ud];
un   = temp(1:length(un));
ui   = temp(length(un)+1:end);
u(Dlist) = ud;
u(Ilist) = ui;
u(Nlist) = un;

Compute the fluxes through Dirichlet sides

Fd = Add * ud + Adi * ui + Adn*un - bd;

Compute the gradient of the solution 

[gx, gy] = bim2c_pde_gradient(mesh,u);

Compute the internal Advection-Diffusion flux

[jxglob,jyglob] = bim2c_global_flux(mesh,u,alfa,gamma,eta,beta);

Save data for later visualization

fpl_dx_write_field("dxdata",mesh,[gx; gy]',"Gradient",1,2,1);
fpl_vtk_write_field ("vtkdata", mesh, {}, {[gx; gy]', "Gradient"}, 1);

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Functions List

Function Reference: bim1a_advection_diffusion

Function File: [A] = bim1a_advection_diffusion(mesh,alpha,gamma,eta,beta)

Build the Scharfetter-Gummel stabilized stiffness matrix for a diffusion-advection problem.

The equation taken into account is:

- div (alpha * gamma (eta grad (u) - beta u)) = f

where alpha is an element-wise constant scalar function, eta and gamma are piecewise linear conforming scalar functions, beta is an element-wise constant vector function.

Instead of passing the vector field beta directly one can pass a piecewise linear conforming scalar function phi as the last input. In such case beta = grad phi is assumed.

If phi is a single scalar value beta is assumed to be 0 in the whole domain.

See also: bim1a_rhs, bim1a_reaction, bim1a_laplacian, bim2a_advection_diffusion

Source Code: bim1a_advection_diffusion

bim-1.1.8/docs/bim1a_advection_upwind.html000066400000000000000000000317611502773057700205460ustar00rootroot00000000000000 PDE Solver using a Finite Element/Finite Volume approach: bim1a_advection_upwind

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Function Reference: bim1a_advection_upwind

Function File: [A] = bim1a_advection_upwind (mesh, beta)

Build the UW stabilized stiffness matrix for an advection problem.

The equation taken into account is:

(beta u)’ = f

where beta is an element-wise constant.

Instead of passing the vector field beta directly one can pass a piecewise linear conforming scalar function phi as the last input. In such case beta = grad phi is assumed.

If phi is a single scalar value beta is assumed to be 0 in the whole domain.

See also: bim1a_rhs, bim1a_reaction, bim1a_laplacian, bim2a_advection_diffusion

Source Code: bim1a_advection_upwind

bim-1.1.8/docs/bim1a_axisymmetric_advection_diffusion.html000066400000000000000000000336001502773057700240160ustar00rootroot00000000000000 PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_advection_diffusion

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Functions List

Function Reference: bim1a_axisymmetric_advection_diffusion

Function File: [A] = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta)

Build the Scharfetter-Gummel stabilized stiffness matrix for a diffusion-advection problem in cylindrical coordinates with axisymmetric configuration. Rotational symmetry is assumed with respect to be the vertical axis r=0. Only grids that DO NOT contain r=0 are admissible.

 
   |   |-------|   OK       |-------|   |   OK        |--|-----|   NO!
  r=0                                  r=0              r=0


 

 The equation taken into account is:



 - 1/r * d/dr (alpha * gamma (eta du/dr - beta u)) = f



 where alpha is an element-wise constant scalar function,
 eta and gamma are piecewise linear conforming scalar
 functions, beta is an element-wise constant vector function.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain. 



 See also: 
  bim1a_axisymmetric_rhs, 
  bim1a_axisymmetric_reaction, 
  bim1a_axisymmetric_laplacian, 
  bim2a_axisymmetric_advection_diffusion



Source Code: 
  bim1a_axisymmetric_advection_diffusion



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_axisymmetric_advection_upwind.html000066400000000000000000000323431502773057700233410ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_advection_upwind
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_axisymmetric_advection_upwind
                

              

            

            




Function File: [A] = bim1a_axisymmetric_advection_upwind (mesh, beta)





 Build the Upwind stabilized stiffness matrix for an advection problem 
 in cylindrical coordinates with axisymmetric configuration.

 



 The equation taken into account is:



 1/r * (r * beta u)’ = f



 where beta is an element-wise constant.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain. 



 See also: 
  bim1a_axisymmetric_advection_diffusion, 
  bim1a_axisymmetric_rhs, 
  bim1a_axisymmetric_reaction, 
  bim1a_axisymmetric_laplacian



Source Code: 
  bim1a_axisymmetric_advection_upwind



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_axisymmetric_laplacian.html000066400000000000000000000325251502773057700217250ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_axisymmetric_laplacian
                

              

            

            




Function File: A = bim1a_axisymmetric_laplacian (mesh,epsilon,kappa)





 Build the standard finite element stiffness matrix for a diffusion
 problem in cylindrical coordinates with axisymmetric configuration. 
 Rotational symmetry is assumed with respect to be the vertical
 axis r=0. Only grids that DO NOT contain r=0 are admissible.





 
   |   |-------|   OK       |--|-----|   NO!
  r=0                         r=0




 The equation taken into account is:



 - 1/r * (r * epsilon * kappa ( u’ ))’ = f

 

 where epsilon is an element-wise constant scalar function,
 while kappa is a piecewise linear conforming scalar function.



 See also: 
  bim1a_axisymmetric_rhs, 
  bim1a_axisymmetric_reaction, 
  bim1a_axisymmetric_advection_diffusion, 
  bim2a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim1a_axisymmetric_laplacian



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_axisymmetric_reaction.html000066400000000000000000000317541502773057700216100ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_reaction
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_axisymmetric_reaction
                

              

            

            




Function File: [C] =  bim1a_axisymmetric_reaction(mesh,delta,zeta)





 Build the lumped finite element mass matrix for a diffusion
 problem in cylindrical coordinates with axisymmetric configuration. 





 The equation taken into account is:



 delta * zeta * u = f

 

 where delta is an element-wise constant scalar function, while
 zeta is a piecewise linear conforming scalar function.



 See also: 
  bim1a_axisymmetric_rhs, 
  bim1a_axisymmetric_advection_diffusion, 
  bim1a_axisymmetric_laplacian, 
  bim2a_reaction, 
  bim3a_reaction



Source Code: 
  bim1a_axisymmetric_reaction



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_axisymmetric_rhs.html000066400000000000000000000314771502773057700206020ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_axisymmetric_rhs
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_axisymmetric_rhs
                

              

            

            




Function File: [b] =  bim1a_rhs(mesh,f, g)





 Build the finite element right-hand side of a diffusion problem
 employing mass-lumping.





 The equation taken into account is:



 delta * u = f * g

 

 where f is an element-wise constant scalar function, while
 g is a piecewise linear conforming scalar function.

 

 See also: 
  bim1a_reaction, 
  bim1a_advection_diffusion, 
  bim1a_laplacian, 
  bim2a_reaction, 
  bim3a_reaction



Source Code: 
  bim1a_axisymmetric_rhs



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_laplacian.html000066400000000000000000000315131502773057700171230ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_laplacian
                

              

            

            




Function File: A = bim1a_laplacian (mesh,epsilon,kappa)





 Build the standard finite element stiffness matrix for a diffusion
 problem. 





 The equation taken into account is:



 - (epsilon * kappa ( u’ ))’ = f

 

 where epsilon is an element-wise constant scalar function,
 while kappa is a piecewise linear conforming scalar function.



 See also: 
  bim1a_rhs, 
  bim1a_reaction, 
  bim1a_advection_diffusion, 
  bim2a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim1a_laplacian



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_reaction.html000066400000000000000000000314421502773057700170040ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_reaction
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_reaction
                

              

            

            




Function File: [C] =  bim1a_reaction(mesh,delta,zeta)





 Build the lumped finite element mass matrix for a diffusion
 problem. 





 The equation taken into account is:



 delta * zeta * u = f

 

 where delta is an element-wise constant scalar function, while
 zeta is a piecewise linear conforming scalar function.



 See also: 
  bim1a_rhs, 
  bim1a_advection_diffusion, 
  bim1a_laplacian, 
  bim2a_reaction, 
  bim3a_reaction



Source Code: 
  bim1a_reaction



            

          

        

      

    


  

bim-1.1.8/docs/bim1a_rhs.html000066400000000000000000000314131502773057700157720ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1a_rhs
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1a_rhs
                

              

            

            




Function File: [b] =  bim1a_rhs(mesh,f, g)





 Build the finite element right-hand side of a diffusion problem
 employing mass-lumping.





 The equation taken into account is:



 delta * u = f * g

 

 where f is an element-wise constant scalar function, while
 g is a piecewise linear conforming scalar function.

 

 See also: 
  bim1a_reaction, 
  bim1a_advection_diffusion, 
  bim1a_laplacian, 
  bim2a_reaction, 
  bim3a_reaction



Source Code: 
  bim1a_rhs



            

          

        

      

    


  

bim-1.1.8/docs/bim1c_elem_to_nodes.html000066400000000000000000000316361502773057700200230ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1c_elem_to_nodes
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1c_elem_to_nodes
                

              

            

            




Function File: u_nod = bim1c_elem_to_nodes (mesh, u_el)


Function File: u_nod = bim1c_elem_to_nodes (m_el, u_el)


Function File: [u_nod, m_el] = bim1c_elem_to_nodes ( ... )





 Compute interpolated values at nodes u_nod given values at element mid-points u_el.
 If called with more than one output, also return the interpolation matrix m_el such that
 u_nod = m_el * u_el.
 If repeatedly performing interpolation on the same mesh the matrix m_el obtained by a previous call 
 to bim1c_elem_to_nodes may be passed as input to avoid unnecessary computations.






Source Code: 
  bim1c_elem_to_nodes




            

          

        

      

    


  

bim-1.1.8/docs/bim1c_norm.html000066400000000000000000000315761502773057700161650ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim1c_norm
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim1c_norm
                

              

            

            




Function File: [norm_u] =  bim1c_norm(mesh,u,norm_type)





 Compute the norm_type-norm of function u on the domain described
 by the triangular grid mesh.





 The input function u can be either a piecewise linear conforming scalar
 function or an elementwise constant scalar or vector function.



 The string parameter norm_type can be one among ’L2’, ’H1’ and ’inf’.



 Should the input function be piecewise constant, the H1 norm will not be 
 computed and the function will return an error message.



 See also: 
  bim2c_norm, 
  bim3c_norm



Source Code: 
  bim1c_norm



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_advection_diffusion.html000066400000000000000000000337421502773057700212300ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_advection_diffusion
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_advection_diffusion
                

              

            

            




Function File: [A] =  bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta)





 Build the Scharfetter-Gummel stabilized stiffness matrix for a
 diffusion-advection problem. 

 



 The equation taken into account is:



 - div (alpha * gamma (eta grad (u) - beta u )) = f



 where alpha is an element-wise constant scalar function,
 eta and gamma are piecewise linear conforming scalar
 functions, beta is an element-wise constant vector function.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain.

 

 Example:
 
 
 mesh = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
 mesh = bim2c_mesh_properties(mesh);
 x    = mesh.p(1,:)';

 Dnodes    = bim2c_unknowns_on_side(mesh,[2,4]);
 Nnodes    = columns(mesh.p);
 Nelements = columns(mesh.t);
 Varnodes  = setdiff(1:Nnodes,Dnodes);

 alpha  = ones(Nelements,1);
 eta    = .1*ones(Nnodes,1);
 beta   = [ones(1,Nelements);zeros(1,Nelements)];
 gamma  = ones(Nnodes,1);
 f      = bim2a_rhs(mesh,ones(Nnodes,1),ones(Nelements,1));

 S   = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
 u   = zeros(Nnodes,1);
 uex = x - (exp(10*x)-1)/(exp(10)-1);
 
 u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
 
 assert(u,uex,1e-7)
 



 See also: 
  bim2a_rhs, 
  bim2a_reaction, 
  bim2c_mesh_properties



Source Code: 
  bim2a_advection_diffusion



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_advection_upwind.html000066400000000000000000000316771502773057700205550ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_advection_upwind
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_advection_upwind
                

              

            

            




Function File: [A] =  bim2a_advection_upwind (mesh, beta)





 Build the UW stabilized stiffness matrix for an advection problem. 

 



 The equation taken into account is:



 div (beta u) = f



 where beta is an element-wise constant vector function.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain.

 

 See also: 
  bim2a_rhs, 
  bim2a_reaction, 
  bim2c_mesh_properties



Source Code: 
  bim2a_advection_upwind



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_advection_diffusion.html000066400000000000000000000337511502773057700240260ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_advection_diffusion
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_advection_diffusion
                

              

            

            




Function File: [A] =  bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta)





 Build the Scharfetter-Gummel stabilized stiffness matrix for a
 diffusion-advection problem in cylindrical coordinates with axisymmetric 
 configuration. Rotational symmetry is assumed with respect to be the vertical
 axis r=0. Only plane geometries that DO NOT intersect the symmetry axis 
 are admitted.





 
    |   ____                 _|____ 
    |  |    \               \ |    |
  z |  |     \  OK           \|    |   NO!
    |  |______\               |\___|
    |     r                   |




 The equation taken into account is:



 1/r * d(r * Fr)/dr + dFz/dz = f



 with



 F = [Fr, Fz]’ = - alpha * gamma ( eta grad (u) - beta u )



 where alpha is an element-wise constant scalar function,
 eta and gamma are piecewise linear conforming scalar
 functions, beta is an element-wise constant vector function.



 Instead of passing the vector field beta directly, one can pass
 a piecewise linear conforming scalar function  phi as the last
 input. In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain.



 See also: 
  bim2a_axisymmetric_rhs, 
  bim2a_axisymmetric_reaction, 
  bim2a_advection_diffusion, 
  bim2c_mesh_properties



Source Code: 
  bim2a_axisymmetric_advection_diffusion



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_advection_upwind.html000066400000000000000000000324031502773057700233370ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_advection_upwind
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_advection_upwind
                

              

            

            




Function File: [A] =  bim2a_axisymmetric_advection_upwind (mesh, beta)





 Build the Upwind stabilized stiffness matrix for an advection problem 
 in cylindrical coordinates with axisymmetric configuration.

 



 The equation taken into account is:



 1/r * d/dr (r * beta_r u) + d/dz (beta_z u) = f



 where beta is an element-wise constant vector function.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi is assumed.



 If phi is a single scalar value beta is assumed to be 0
 in the whole domain.

 

 See also: 
  bim2a_axisymmetric_rhs, 
  bim2a_axisymmetric_reaction, 
  bim2a_axisymmetric_advection_diffusion, 
  bim2c_mesh_properties



Source Code: 
  bim2a_axisymmetric_advection_upwind



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_boundary_mass.html000066400000000000000000000320751502773057700226500ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_boundary_mass
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_boundary_mass
                

              

            

            




Function File: [M] =  bim2a_axisymmetric_boundary_mass(mesh,sidelist,nodelist)





 Build the lumped boundary mass matrix needed to apply Robin and Neumann
 boundary conditions in a problem in cylindrical coordinates with 
 axisymmetric configuration.





 The vector sidelist contains the list of the side edges
 contributing to the mass matrix.



 The optional argument nodelist contains the list of the
 degrees of freedom on the boundary.



 See also: 
  bim2a_axisymmetric_rhs, 
  bim2a_axisymmetric_advection_diffusion, 
  bim2a_axisymmetric_laplacian, 
  bim2a_axisymmetric_reaction, 
  bim2a_boundary_mass



Source Code: 
  bim2a_axisymmetric_boundary_mass



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_laplacian.html000066400000000000000000000331021502773057700217160ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_laplacian
                

              

            

            




Function File: A = bim2a_axisymmetric_laplacian (mesh,epsilon,kappa)





 Build the standard finite element stiffness matrix for a diffusion
 problem in cylindrical coordinates with axisymmetric configuration.
 Rotational symmetry is assumed with respect to be the vertical axis r=0. 
 Only plane geometries that DO NOT intersect the symmetry axis are admitted.





 
    |   ____                 _|____ 
    |  |    \               \ |    |
  z |  |     \  OK           \|    |   NO!
    |  |______\               |\___|
    |     r                   |




 The equation taken into account is:



 1/r * d(r * Fr)/dr + dFz/dz = f



 with



 F = [Fr, Fz]’ = - epsilon * kappa grad (u)

 

 where epsilon is an element-wise constant scalar function,
 while kappa is a piecewise linear conforming scalar function.



 See also: 
  bim2a_axisymmetric_rhs, 
  bim2a_axisymmetric_reaction, 
  bim2a_axisymmetric_advection_diffusion, 
  bim2a_laplacian, 
  bim1a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim2a_axisymmetric_laplacian



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_reaction.html000066400000000000000000000320061502773057700216000ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_reaction
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_reaction
                

              

            

            




Function File: [C] =  bim2a_axisymmetric_reaction(mesh,delta,zeta)





 Build the lumped finite element mass matrix for a diffusion
 problem in cylindrical coordinates with axisymmetric configuration.





 The equation taken into account is:



 delta * zeta * u = f

 

 where delta is an element-wise constant scalar function, while
 zeta is a piecewise linear conforming scalar function.



 See also: 
  bim2a_rhs, 
  bim2a_axisymmetric_advection_diffusion, 
  bim2a_axisymmetric_laplacian, 
  bim2a_reaction, 
  bim1a_reaction, 
  bim3a_reaction



Source Code: 
  bim2a_axisymmetric_reaction



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_axisymmetric_rhs.html000066400000000000000000000316601502773057700205750ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_axisymmetric_rhs
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_axisymmetric_rhs
                

              

            

            




Function File: [b] =  bim2a_axisymmetric_rhs(mesh,f,g)





 Build the finite element right-hand side of a diffusion problem
 in cylindrical coordinates with axisymmetric configuration
 employing mass-lumping.





 The equation taken into account is:



 delta * u = f * g

 

 where f is an element-wise constant scalar function, while
 g is a piecewise linear conforming scalar function.

 

 See also: 
  bim2a_axisymmetric_reaction, 
  bim2a_axisymmetric_advection_diffusion, 
  bim2a_axisymmetric_laplacian, 
  bim1a_axisymmetric_rhs



Source Code: 
  bim2a_axisymmetric_rhs



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_boundary_mass.html000066400000000000000000000314021502773057700200430ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_boundary_mass
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_boundary_mass
                

              

            

            




Function File: [M] =  bim2a_boundary_mass(mesh,sidelist,nodelist)





 Build the lumped boundary mass matrix needed to apply Robin boundary
 conditions.   





 The vector sidelist contains the list of the side edges
 contributing to the mass matrix.



 The optional argument nodelist contains the list of the
 degrees of freedom on the boundary.



 See also: 
  bim2a_rhs, 
  bim2a_advection_diffusion, 
  bim2a_laplacian, 
  bim2a_reaction



Source Code: 
  bim2a_boundary_mass



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_laplacian.html000066400000000000000000000350251502773057700171260ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_laplacian
                

              

            

            




Function File: A = bim2a_laplacian (mesh,epsilon,kappa)





 Build the standard finite element stiffness matrix for a diffusion
 problem. 





 The equation taken into account is:



 - div (epsilon * kappa grad (u)) = f

 

 where epsilon is an element-wise constant scalar function,
 while kappa is a piecewise linear conforming scalar function.



 See also: 
  bim2a_rhs, 
  bim2a_reaction, 
  bim2a_advection_diffusion, 
  bim1a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim2a_laplacian


        

          

            

              

                

                  

                  Example: 1
                  

                

              

            

            

              

                

                  

                     
                    

 m = msh2m_structured_mesh (0:.1:2*pi, 0:.1:2*pi, 1, 1:4, 'random');
 m = bim2c_mesh_properties (m);
 kappa = 2 + sin (m.p(1, :)');
 f     = kappa .* cos (m.p(2, :)');
 uex   = cos (m.p(2, :)');
 A = bim2a_laplacian (m, 3./(sum(1./kappa(m.t(1:3, :)), 1)), 1);
 b = bim2a_rhs (m, 1, f);
 dnodes = bim2c_unknowns_on_side (m, 1:4);
 inodes = setdiff (1:columns(m.p), dnodes);
 u = uex;
 u(inodes) = A(inodes, inodes) \ (b(inodes)-A(inodes, dnodes) * u(dnodes));
 h = pdesurf (m.p, m.t, u)
 figure
 pdesurf (m.p, m.t, uex)

h = -39.365
                    

                  

                  

                    plotted figure
                  

                  

                    plotted figure
                  


                

              

            

          

        



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_reaction.html000066400000000000000000000314421502773057700170050ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_reaction
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_reaction
                

              

            

            




Function File: [C] =  bim2a_reaction(mesh,delta,zeta)





 Build the lumped finite element mass matrix for a diffusion
 problem. 





 The equation taken into account is:



 delta * zeta * u = f

 

 where delta is an element-wise constant scalar function, while
 zeta is a piecewise linear conforming scalar function.



 See also: 
  bim2a_rhs, 
  bim2a_advection_diffusion, 
  bim2a_laplacian, 
  bim1a_reaction, 
  bim3a_reaction



Source Code: 
  bim2a_reaction



            

          

        

      

    


  

bim-1.1.8/docs/bim2a_rhs.html000066400000000000000000000314121502773057700157720ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2a_rhs
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2a_rhs
                

              

            

            




Function File: [b] =  bim2a_rhs(mesh,f,g)





 Build the finite element right-hand side of a diffusion problem
 employing mass-lumping.





 The equation taken into account is:



 delta * u = f * g

 

 where f is an element-wise constant scalar function, while
 g is a piecewise linear conforming scalar function.

 

 See also: 
  bim2a_reaction, 
  bim2a_advection_diffusion, 
  bim2a_laplacian, 
  bim1a_reaction, 
  bim3a_reaction



Source Code: 
  bim2a_rhs



            

          

        

      

    


  

bim-1.1.8/docs/bim2c_global_flux.html000066400000000000000000000325631502773057700175060ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_global_flux
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_global_flux
                

              

            

            




Function File: [jx,jy] =  bim2c_global_flux(mesh,u,alpha,gamma,eta,beta)



 

 Compute the flux associated with the Scharfetter-Gummel approximation
 of the scalar field u.





 The vector field is defined as:



 J(u) = alpha* gamma * (eta * grad u - beta * u))

 

 where alpha is an element-wise constant scalar function,
 eta and gamma are piecewise linear conforming scalar
 functions, while beta is element-wise constant vector function.



 J(u) is an element-wise constant vector function.



 Instead of passing the vector field beta directly one can pass
 a piecewise linear conforming scalar function  phi as the last
 input.  In such case beta = grad phi  is assumed.  If
 phi is a single scalar value beta  is assumed to be 0 in
 the whole domain.



 See also: 
  bim2c_pde_gradient, 
  bim2a_advection_diffusion



Source Code: 
  bim2c_global_flux



            

          

        

      

    


  

bim-1.1.8/docs/bim2c_intrp.html000066400000000000000000000307331502773057700163410ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_intrp
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_intrp
                

              

            

            




Function File: data = bim2c_intrp (msh, n_data, e_data, points)





 Compute interpolated values of multicomponent node centered field n_data and/or
 cell centered field n_data at an arbitrary set of points whose coordinates are given in the 
 n_by_2 matrix points. 






Source Code: 
  bim2c_intrp




            

          

        

      

    


  

bim-1.1.8/docs/bim2c_mesh_properties.html000066400000000000000000000312441502773057700204130ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_mesh_properties
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_mesh_properties
                

              

            

            




Function File: [omesh] =  bim2c_mesh_properties(imesh)





 Compute the properties of imesh needed by BIM method and append
 them to omesh as fields.





 See also: 
  bim2a_reaction, 
  bim2a_advection_diffusion, 
  bim2a_rhs, 
  bim2a_laplacian, 
  bim2a_boundary_mass



Source Code: 
  bim2c_mesh_properties



            

          

        

      

    


  

bim-1.1.8/docs/bim2c_norm.html000066400000000000000000000317541502773057700161640ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_norm
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_norm
                

              

            

            




Function File: [norm_u] =  bim2c_norm(mesh,u,norm_type)





 Compute the norm_type-norm of function u on the domain described
 by the triangular grid mesh.





 The input function u can be either a piecewise linear conforming scalar
 function or an elementwise constant scalar or vector function.



 The string parameter norm_type can be one among ’L2’, ’H1’ and ’inf’.



 Should the input function be piecewise constant, the H1 norm will not be 
 computed and the function will return an error message.



 For the numerical integration of the L2 norm the second order middle point
 quadrature rule is used.



 See also: 
  bim1c_norm, 
  bim3c_norm



Source Code: 
  bim2c_norm



            

          

        

      

    


  

bim-1.1.8/docs/bim2c_pde_gradient.html000066400000000000000000000306551502773057700176350ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_pde_gradient
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_pde_gradient
                

              

            

            




Function File: [gx,gy] =  bim2c_pde_gradient(mesh,u)





 Compute the gradient of the piecewise linear conforming scalar
 function u.





 See also: 
  bim2c_global_flux



Source Code: 
  bim2c_pde_gradient



            

          

        

      

    


  

bim-1.1.8/docs/bim2c_tri_to_nodes.html000066400000000000000000000316511502773057700176750ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_tri_to_nodes
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_tri_to_nodes
                

              

            

            




Function File: u_nod = bim2c_tri_to_nodes (mesh, u_tri)


Function File: u_nod = bim2c_tri_to_nodes (m_tri, u_tri)


Function File: [u_nod, m_tri] = bim2c_tri_to_nodes ( ... )





 Compute interpolated values at triangle nodes u_nod given values at triangle mid-points u_tri.
 If called with more than one output, also return the interpolation matrix m_tri such that
 u_nod = m_tri * u_tri.
 If repeatedly performing interpolation on the same mesh the matrix m_tri obtained by a previous call 
 to bim2c_tri_to_nodes may be passed as input to avoid unnecessary computations.






Source Code: 
  bim2c_tri_to_nodes




            

          

        

      

    


  

bim-1.1.8/docs/bim2c_unknowns_on_side.html000066400000000000000000000310461502773057700205650ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim2c_unknowns_on_side
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim2c_unknowns_on_side
                

              

            

            




Function File: [nodelist] =  bim2c_unknowns_on_side(mesh,sidelist)





 Return the list of the mesh nodes that lie on the geometrical sides
 specified in sidelist.





 See also: 
bim3c_unknown_on_faces, 
  bim2c_pde_gradient, 
  bim2c_global_flux



Source Code: 
  bim2c_unknowns_on_side



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_advection_diffusion.html000066400000000000000000000315001502773057700212170ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_advection_diffusion
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_advection_diffusion
                

              

            

            




Function File: [A] =  bim3a_advection_diffusion (mesh, alpha, v)





 Build the Scharfetter-Gummel stabilized stiffness matrix for a
 diffusion-advection problem. 

 



 The equation taken into account is:



 - div (alpha ( grad (u) - grad (v) u)) = f



 where v is a piecewise linear continuous scalar
 functions and alpha is a piecewise constant scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_reaction, 
  bim3a_laplacian, 
  bim3c_mesh_properties



Source Code: 
  bim3a_advection_diffusion



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_boundary_mass.html000066400000000000000000000314711502773057700200520ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_boundary_mass
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_boundary_mass
                

              

            

            




Function File: [M] =  bim3a_boundary_mass(mesh,facelist,nodelist)





 Build the lumped boundary mass matrix needed to apply Robin boundary
 conditions.





 The vector facelist contains the list of the faces contributing
 to the mass matrix.



 The optional argument nodelist contains the list of the
 degrees of freedom on the boundary.



 See also: 
  bim3a_rhs, 
  bim3a_advection_diffusion, 
  bim3a_laplacian, 
  bim3a_reaction, 
  bim2a_boundary_mass



Source Code: 
  bim3a_boundary_mass



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_laplacian.html000066400000000000000000000314021502773057700171220ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_laplacian
                

              

            

            




Function File: A = bim3a_laplacian (mesh, epsilon, kappa)





 Build the standard finite element stiffness matrix for a diffusion
 problem. 





 The equation taken into account is:



 - (epsilon * kappa ( u’ ))’ = f

 

 where epsilon is an element-wise constant scalar function,
 while kappa is a piecewise linear conforming scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_reaction, 
  bim2a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim3a_laplacian



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_osc_advection_diffusion.html000066400000000000000000000320571502773057700220730ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_osc_advection_diffusion
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_osc_advection_diffusion
                

              

            

            




Function File: [A] = bim3a_osc_advection_diffusion (mesh, alpha, v)





 Build the Scharfetter-Gummel stabilized OSC stiffness 
 matrix for a diffusion-advection problem. 

 



 For details on the Orthogonal Subdomain Collocation (OSC) method
 see: M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998.



 The equation taken into account is:



 - div (alpha ( grad (u) - grad (v) u)) = f



 where v is a piecewise linear continuous scalar
 functions and alpha is a piecewise constant scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_osc_laplacian, 
  bim3a_reaction, 
  bim3a_laplacian, 
  bim3c_mesh_properties



Source Code: 
  bim3a_osc_advection_diffusion



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_osc_laplacian.html000066400000000000000000000314641502773057700177760ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_osc_laplacian
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_osc_laplacian
                

              

            

            




Function File: A = bim3a_osc_laplacian (mesh, epsilon)





 Build the osc finite element stiffness matrix for a diffusion
 problem. 





 For details on the Orthogonal Subdomain Collocation (OSC) method
 see: M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998. 



 The equation taken into account is:



 - div (epsilon grad (u)) = f

 

 where epsilon is an element-wise constant scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_reaction, 
  bim2a_laplacian, 
  bim3a_laplacian



Source Code: 
  bim3a_osc_laplacian



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_reaction.html000066400000000000000000000313271502773057700170100ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_reaction
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_reaction
                

              

            

            




Function File: [C] = bim3a_reaction (mesh,delta,zeta)





 Build the lumped finite element mass matrix for a diffusion
 problem. 





 The equation taken into account is:



 delta * zeta * u = f

 

 where delta is an element-wise constant scalar function, while
 zeta is a piecewise linear conforming scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_laplacian, 
  bim2a_reaction, 
  bim3a_reaction



Source Code: 
  bim3a_reaction



            

          

        

      

    


  

bim-1.1.8/docs/bim3a_rhs.html000066400000000000000000000312631502773057700157770ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3a_rhs
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3a_rhs
                

              

            

            




Function File: [b] =  bim3a_rhs (mesh, f, g)





 Build the finite element right-hand side of a diffusion problem
 employing mass-lumping.





 The equation taken into account is:



 delta * u =  f * g

 

 where f is an element-wise constant scalar function, while
 g is a piecewise linear conforming scalar function.

 

 See also: 
  bim3a_reaction, 
bim3_laplacian, 
  bim1a_reaction, 
  bim2a_reaction



Source Code: 
  bim3a_rhs



            

          

        

      

    


  

bim-1.1.8/docs/bim3c_global_flux.html000066400000000000000000000315471502773057700175100ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_global_flux
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3c_global_flux
                

              

            

            




Function File: [F] =  bim3c_global_flux (mesh, u, alpha, v)





 Compute the flux associated with the Scharfetter-Gummel approximation
 of the scalar field u.





 The vector field is defined as:



 F =- alpha ( grad (u) - grad (v) u ) 



 where v is a piecewise linear continuous scalar
 functions and alpha is a piecewise constant scalar function.



 See also: 
  bim3a_rhs, 
  bim3a_reaction, 
  bim3a_laplacian, 
  bim3c_mesh_properties



Source Code: 
  bim3c_global_flux



            

          

        

      

    


  

bim-1.1.8/docs/bim3c_intrp.html000066400000000000000000000307471502773057700163470ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_intrp
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3c_intrp
                

              

            

            




Function File: data = bim3c_intrp (msh, n_data, e_data, points)





 Compute interpolated values of node centered multicomponent node centered field n_data and 
 cell centered field n_data at an arbitrary set of points whos coordinates are given in the 
 n_by_3 matrix  points. 






Source Code: 
  bim3c_intrp




            

          

        

      

    


  

bim-1.1.8/docs/bim3c_mesh_properties.html000066400000000000000000000310321502773057700204070ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_mesh_properties
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3c_mesh_properties
                

              

            

            




Function File: [omesh] =  bim3c_mesh_properties(imesh)





 Compute the properties of imesh needed by BIM method and append
 them to omesh as fields.





 See also: 
  bim3a_reaction, 
  bim3a_rhs, 
  bim3a_laplacian



Source Code: 
  bim3c_mesh_properties



            

          

        

      

    


  

bim-1.1.8/docs/bim3c_norm.html000066400000000000000000000321031502773057700161520ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_norm
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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                Function Reference: bim3c_norm
                

              

            

            




Function File: [norm_u] =  bim3c_norm(mesh,u,norm_type)





 Compute the norm_type-norm of function u on the domain described
 by the tetrahedral grid mesh.





 The input function u can be either a piecewise linear conforming scalar
 function or an elementwise constant scalar or vector function.



 The string parameter norm_type can be one among ’L2’, ’H1’ and ’inf’.



 Should the input function be piecewise constant, the H1 norm will not be 
 computed and the function will return an error message.



 For the numerical integration of the L2 norm the second order quadrature rule
 by Keast is used (ref. P. Keast, Moderate degree tetrahedral quadrature
 formulas, CMAME 55: 339-348 1986).



 See also: 
  bim1c_norm, 
  bim2c_norm



Source Code: 
  bim3c_norm



            

          

        

      

    


  

bim-1.1.8/docs/bim3c_pde_gradient.html000066400000000000000000000306751502773057700176400ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_pde_gradient
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
Categories &

            
Functions List

          

			

				
				
				

				
				

			

			

				
				
				

				
				

			

			

				
				
				

				
				

			


			  

			  

          

            

              

                

                Function Reference: bim3c_pde_gradient
                

              

            

            




Function File: [gx, gy, gz] =  bim3c_pde_gradient(mesh,u)





 Compute the gradient of the piecewise linear conforming scalar
 function u.





 See also: 
  bim3c_global_flux



Source Code: 
  bim3c_pde_gradient



            

          

        

      

    


  

bim-1.1.8/docs/bim3c_tri_to_nodes.html000066400000000000000000000316611502773057700176770ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_tri_to_nodes
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
Categories &

            
Functions List

          

			

				
				
				

				
				

			

			

				
				
				

				
				

			

			

				
				
				

				
				

			


			  

			  

          

            

              

                

                Function Reference: bim3c_tri_to_nodes
                

              

            

            




Function File: u_nod = bim3c_tri_to_nodes (mesh, u_tri)


Function File: u_nod = bim3c_tri_to_nodes (m_tri, u_tri)


Function File: [u_nod, m_tri] = bim3c_tri_to_nodes ( ... )





 Compute interpolated values at triangle nodes u_nod given values at tetrahedral centers of mass u_tri.
 If called with more than one output, also return the interpolation matrix m_tri such that
 u_nod = m_tri * u_tri.
 If repeatedly performing interpolation on the same mesh the matrix m_tri obtained by a previous call 
 to bim2c_tri_to_nodes may be passed as input to avoid unnecessary computations.






Source Code: 
  bim3c_tri_to_nodes




            

          

        

      

    


  

bim-1.1.8/docs/bim3c_unknowns_on_faces.html000066400000000000000000000310531502773057700207210ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bim3c_unknowns_on_faces
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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Functions List

          

			

				
				
				

				
				

			

			

				
				
				

				
				

			

			

				
				
				

				
				

			


			  

			  

          

            

              

                

                Function Reference: bim3c_unknowns_on_faces
                

              

            

            




Function File: [nodelist] =  bim3c_unknowns_on_faces(mesh,facelist)





 Return the list of the mesh nodes that lie on the geometrical faces
 specified in facelist.





 See also: 
bim3c_unknown_on_faces, 
  bim2c_pde_gradient, 
  bim2c_global_flux



Source Code: 
  bim3c_unknowns_on_faces



            

          

        

      

    


  

bim-1.1.8/docs/bimu_bernoulli.html000066400000000000000000000305031502773057700171330ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bimu_bernoulli
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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Functions List

          

			

				
				
				

				
				

			

			

				
				
				

				
				

			

			

				
				
				

				
				

			


			  

			  

          

            

              

                

                Function Reference: bimu_bernoulli
                

              

            

            




Function File: [bp, bn] = bimu_bernoulli (x)





 Compute the values of the Bernoulli function corresponding to x
 and - x arguments. 

 



 See also: 
  bimu_logm



Source Code: 
  bimu_bernoulli



            

          

        

      

    


  

bim-1.1.8/docs/bimu_logm.html000066400000000000000000000304671502773057700161070ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach: bimu_logm
    
    
    
    
    
    
    
    
  
  
    

      

        
      

    

    

      

        

          

            
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Functions List

          

			

				
				
				

				
				

			

			

				
				
				

				
				

			

			

				
				
				

				
				

			


			  

			  

          

            

              

                

                Function Reference: bimu_logm
                

              

            

            




Function File: [T] = bimu_logm (t1,t2)



 

 Input:
 
<

ul class="toc">

  • - t1:
 
  • - t2:
 
    • 


     Output:
 
      

    • - T:
 
    


     See also: 
bimu_bern

    

    Source Code: 
  bimu_logm

    

            
    
          
    
        
    
      
    
    
    

  

bim-1.1.8/docs/index.html000066400000000000000000000533361502773057700152440ustar00rootroot00000000000000

  
    PDE Solver using a Finite Element/Finite Volume approach
    
    
    
    
    
    
    
    
  
  
    
    
      
    
        
      
    
    
    
    
    
      
    
        
    
          
    
            
    
              bim
            
    
            
    
              
    bim
    
              1.1.6 2022-07-22
              
    
                Package for solving Diffusion Advection Reaction (DAR) Partial Differential Equations
              
    
            
    
          
    
        
    
        
    
           
    Select Category:
             
           
    

           
    
             Matrix assembly
           
    
           
    
             
               
    
                 
                   
                   bim1a_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-advection problem.
               
    
               
    
                 
                   
                   bim1a_advection_upwind
                   
                 
                 Build the UW stabilized stiffness matrix for an advection problem.
               
    
               
    
                 
                   
                   bim1a_axisymmetric_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-advection problem in cylindrical coordinates with axisymmetric
configuration.
               
    
               
    
                 
                   
                   bim1a_axisymmetric_advection_upwind
                   
                 
                 Build the Upwind stabilized stiffness matrix for an advection problem in
cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim2a_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-advection problem.
               
    
               
    
                 
                   
                   bim2a_advection_upwind
                   
                 
                 Build the UW stabilized stiffness matrix for an advection problem.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-advection problem in cylindrical coordinates with axisymmetric
configuration.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_advection_upwind
                   
                 
                 Build the Upwind stabilized stiffness matrix for an advection problem in
cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim3a_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized stiffness matrix for a
diffusion-advection problem.
               
    
               
    
                 
                   
                   bim3a_osc_advection_diffusion
                   
                 
                 Build the Scharfetter-Gummel stabilized OSC stiffness matrix for a
diffusion-advection problem.
               
    
               
    
                 
                   
                   bim1a_laplacian
                   
                 
                 Build the standard finite element stiffness matrix for a diffusion
problem.
               
    
               
    
                 
                   
                   bim1a_axisymmetric_laplacian
                   
                 
                 Build the standard finite element stiffness matrix for a diffusion
problem in cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim2a_laplacian
                   
                 
                 Build the standard finite element stiffness matrix for a diffusion
problem.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_laplacian
                   
                 
                 Build the standard finite element stiffness matrix for a diffusion
problem in cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim3a_laplacian
                   
                 
                 Build the standard finite element stiffness matrix for a diffusion
problem.
               
    
               
    
                 
                   
                   bim3a_osc_laplacian
                   
                 
                 Build the osc finite element stiffness matrix for a diffusion problem.
               
    
               
    
                 
                   
                   bim1a_reaction
                   
                 
                 Build the lumped finite element mass matrix for a diffusion problem.
               
    
               
    
                 
                   
                   bim1a_axisymmetric_reaction
                   
                 
                 Build the lumped finite element mass matrix for a diffusion problem in
cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim2a_reaction
                   
                 
                 Build the lumped finite element mass matrix for a diffusion problem.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_reaction
                   
                 
                 Build the lumped finite element mass matrix for a diffusion problem in
cylindrical coordinates with axisymmetric configuration.
               
    
               
    
                 
                   
                   bim3a_reaction
                   
                 
                 Build the lumped finite element mass matrix for a diffusion problem.
               
    
               
    
                 
                   
                   bim1a_rhs
                   
                 
                 Build the finite element right-hand side of a diffusion problem
employing mass-lumping.
               
    
               
    
                 
                   
                   bim1a_axisymmetric_rhs
                   
                 
                 Build the finite element right-hand side of a diffusion problem
employing mass-lumping.
               
    
               
    
                 
                   
                   bim2a_rhs
                   
                 
                 Build the finite element right-hand side of a diffusion problem
employing mass-lumping.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_rhs
                   
                 
                 Build the finite element right-hand side of a diffusion problem in
cylindrical coordinates with axisymmetric configuration employing
mass-lumping.
               
    
               
    
                 
                   
                   bim3a_rhs
                   
                 
                 Build the finite element right-hand side of a diffusion problem
employing mass-lumping.
               
    
               
    
                 
                   
                   bim2a_boundary_mass
                   
                 
                 Build the lumped boundary mass matrix needed to apply Robin boundary
conditions.
               
    
               
    
                 
                   
                   bim2a_axisymmetric_boundary_mass
                   
                 
                 Build the lumped boundary mass matrix needed to apply Robin and Neumann
boundary conditions in a problem in cylindrical coordinates with
axisymmetric configuration.
               
    
               
    
                 
                   
                   bim3a_boundary_mass
                   
                 
                 Build the lumped boundary mass matrix needed to apply Robin boundary
conditions.
               
    
                 
           
    
           
    
             Pre-processing and Post-processing computations
           
    
           
    
             
               
    
                 
                   
                   bim2c_mesh_properties
                   
                 
                 Compute the properties of IMESH needed by BIM method and append them to
OMESH as fields.
               
    
               
    
                 
                   
                   bim3c_mesh_properties
                   
                 
                 Compute the properties of IMESH needed by BIM method and append them to
OMESH as fields.
               
    
               
    
                 
                   
                   bim2c_unknowns_on_side
                   
                 
                 Return the list of the mesh nodes that lie on the geometrical sides
specified in SIDELIST.
               
    
               
    
                 
                   
                   bim3c_unknowns_on_faces
                   
                 
                 Return the list of the mesh nodes that lie on the geometrical faces
specified in FACELIST.
               
    
               
    
                 
                   
                   bim2c_pde_gradient
                   
                 
                 Compute the gradient of the piecewise linear conforming scalar function
U.
               
    
               
    
                 
                   
                   bim3c_pde_gradient
                   
                 
                 Compute the gradient of the piecewise linear conforming scalar function
U.
               
    
               
    
                 
                   
                   bim2c_global_flux
                   
                 
                 Compute the flux associated with the Scharfetter-Gummel approximation of
the scalar field U.
               
    
               
    
                 
                   
                   bim3c_global_flux
                   
                 
                 Compute the flux associated with the Scharfetter-Gummel approximation of
the scalar field U.
               
    
               
    
                 
                   
                   bim1c_elem_to_nodes
                   
                 
                 Compute interpolated values at nodes U_NOD given values at element
mid-points U_EL.
               
    
               
    
                 
                   
                   bim2c_tri_to_nodes
                   
                 
                 Compute interpolated values at triangle nodes U_NOD given values at
triangle mid-points U_TRI.
               
    
               
    
                 
                   
                   bim3c_tri_to_nodes
                   
                 
                 Compute interpolated values at triangle nodes U_NOD given values at
tetrahedral centers of mass U_TRI.
               
    
               
    
                 
                   
                   bim2c_intrp
                   
                 
                 Compute interpolated values of multicomponent node centered field N_DATA
and/or cell centered field N_DATA at an arbitrary set of points whose
coordinates are given in the n_by_2 matrix POINTS.
               
    
               
    
                 
                   
                   bim3c_intrp
                   
                 
                 Compute interpolated values of node centered multicomponent node
centered field N_DATA and cell centered field N_DATA at an arbitrary set
of points whos coordinates are given in the n_by_3 matrix POINTS.
               
    
               
    
                 
                   
                   bim1c_norm
                   
                 
                 Compute the NORM_TYPE-norm of function U on the domain described by the
triangular grid MESH.
               
    
               
    
                 
                   
                   bim2c_norm
                   
                 
                 Compute the NORM_TYPE-norm of function U on the domain described by the
triangular grid MESH.
               
    
               
    
                 
                   
                   bim3c_norm
                   
                 
                 Compute the NORM_TYPE-norm of function U on the domain described by the
tetrahedral grid MESH.
               
    
                 
           
    
           
    
             Utilities
           
    
           
    
             
               
    
                 
                   
                   bimu_bernoulli
                   
                 
                 Compute the values of the Bernoulli function corresponding to X and - X
arguments.
               
    
               
    
                 
                   
                   bimu_logm
                   
                 
                 Input:
   − T1:
   − T2:
               
    
                 
           
    

        
    
      
    
    
    

  

bim-1.1.8/inst/000077500000000000000000000000001502773057700132625ustar00rootroot00000000000000bim-1.1.8/inst/bim1a_advection_diffusion.m000066400000000000000000000077171502773057700205470ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim1a_advection_diffusion(@var{mesh},@var{alpha},@var{gamma},@var{eta},@var{beta})
##
## Build the Scharfetter-Gummel stabilized stiffness matrix for a
## diffusion-advection problem. 
## 
## The equation taken into account is:
##
## - div (@var{alpha} * @var{gamma} (@var{eta} grad (u) - @var{beta} u)) = f
##
## where @var{alpha} is an element-wise constant scalar function,
## @var{eta} and @var{gamma} are piecewise linear conforming scalar
## functions, @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain. 
##
## @seealso{bim1a_rhs, bim1a_reaction, bim1a_laplacian, bim2a_advection_diffusion} 
## @end deftypefn

function A = bim1a_advection_diffusion (x,alpha,gamma,eta,beta)

  ## Check input
  if (nargin != 5)
    error ("bim1a_advection_diffusion: wrong number of input parameters.");
  elseif (! isvector (x))
    error ("bim1a_advection_diffusion: first argument is not a valid vector.");
  endif
  
  nnodes = numel (x);
  nelem  = nnodes - 1;

  ## Turn scalar input to a vector of appropriate size
  if (isscalar (alpha))
    alpha = alpha * ones (nelem, 1);
  endif
  if (isscalar (gamma))
    gamma = gamma * ones (nnodes, 1);
  endif
  if (isscalar (eta))
    eta = eta * ones (nnodes, 1);
  endif
  
  if (! (isvector (alpha) && isvector (gamma) && isvector (eta)))
    error ("bim1a_advection_diffusion: coefficients are not valid vectors.");
  elseif (numel (alpha) != nelem)
    error ("bim1a_advection_diffusion: length of alpha is not equal to the number of elements.");
  elseif (numel (gamma) != nnodes)
    error ("bim1a_advection_diffusion: length of gamma is not equal to the number of nodes.");
  elseif (numel (eta) != nnodes)
    error ("bim1a_advection_diffusion: length of eta is not equal to the number of nodes.");
  endif

  areak = reshape (diff (x), [], 1);
 
  if (numel (beta) == 1)
    vk = 0;
  elseif (numel (beta) == nelem)
    vk = beta .* areak;
  elseif (numel (beta) == nnodes)
    vk = diff (beta);
  else
    error ("bim1a_advection_diffusion: coefficient beta has wrong dimensions.");
  endif
  
  gammaetak = bimu_logm ((gamma .* eta)(1:end-1), (gamma .* eta)(2:end));
  veta      = diff (eta);
  etak      = bimu_logm (eta(1:end-1), eta(2:end));
  ck        = alpha .* gammaetak .* etak ./ areak; 

  [bpk, bmk]  = bimu_bernoulli ((vk - veta) ./ etak);
 
  dm1 = [-(ck.*bmk); NaN]; 
  dp1 = [NaN; -(ck.*bpk)]; 
  d0  = [(ck(1).*bmk(1)); ((ck.*bmk)(2:end) + (ck.*bpk)(1:end-1)); (ck(end).*bpk(end))];
  A   = spdiags([dm1, d0, dp1],-1:1,nnodes,nnodes);

endfunction

%!test
%! x = linspace(0,1,101);
%! A = bim1a_advection_diffusion(x,1,1,1,0);
%! alpha = ones(100,1);
%! gamma = ones(101,1);
%! eta   = gamma;
%! B = bim1a_advection_diffusion(x,alpha,gamma,eta,0);
%! assert(A,B)
bim-1.1.8/inst/bim1a_advection_upwind.m000066400000000000000000000060751502773057700200630ustar00rootroot00000000000000## Copyright (C) 2010-2014  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo Porro       

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = bim1a_advection_upwind (@var{mesh}, @var{beta})
##
## Build the UW stabilized stiffness matrix for an advection problem. 
## 
## The equation taken into account is:
##
##  (@var{beta} u)' = f
##
## where @var{beta} is an element-wise constant.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain. 
##
## @seealso{bim1a_rhs, bim1a_reaction, bim1a_laplacian, bim2a_advection_diffusion} 
## @end deftypefn

function A = bim1a_advection_upwind (x, beta)

  ## Check input
  if nargin != 2
    error("bim1a_advection_upwind: wrong number of input parameters.");
  endif
  
  nnodes = length(x);
  nelem  = nnodes-1;

  if (length(beta) == 1)
    vk = zeros(nelem,1);
  elseif (length(beta) == nelem)
    vk = beta; 
  elseif (length(beta) == nnodes)
    vk = diff(beta);
  else
    error("bim1a_advection_upwind: coefficient beta has wrong dimensions.");
  endif
  
  bmk =  (vk+abs(vk))/2;
  bpk = -(vk-abs(vk))/2;
 
  dm1 = [-bmk; NaN];
  dp1 = [NaN; -bpk]; 
  d0  = [bmk(1); bmk(2:end) + bpk(1:end-1); bpk(end)];
  A   = spdiags([dm1, d0, dp1],-1:1,nnodes,nnodes);

endfunction

%!test
%! n = 200;
%! mesh      = linspace(0,1,n+1)';
%! uex       = @(r) - r.^2 + 1;
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1;  v = 1;  sigma = 0;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*v*ones(Nelements,1);
%! delta  = ones(Nelements,1);
%! zeta   = sigma*ones(Nnodes,1);
%! f      = @(r) 2*D - 2*v.*r + sigma*uex(r);
%! rhs    = bim1a_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_laplacian(mesh,alpha,gamma);
%! A = bim1a_advection_upwind(mesh, beta);
%! R = bim1a_reaction(mesh, delta, zeta);
%! S += (A+R);
%! u = zeros(Nnodes,1); u([1 end]) = uex(mesh([1 end]));
%! u(2:end-1) = S(2:end-1,2:end-1)\(rhs(2:end-1) - S(2:end-1,[1 end])*u([1 end]));
%! assert(u,uex(mesh),1e-3)
bim-1.1.8/inst/bim1a_axisymmetric_advection_diffusion.m000066400000000000000000000151561502773057700233410ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo Porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim1a_axisymmetric_advection_diffusion(@var{mesh},@var{alpha},@var{gamma},@var{eta},@var{beta})
##
## Build the Scharfetter-Gummel stabilized stiffness matrix for a
## diffusion-advection problem in cylindrical coordinates with axisymmetric 
## configuration. Rotational symmetry is assumed with respect to be the vertical
## axis r=0. Only grids that DO NOT contain r=0 are admissible.
##
##@example
##@group
##   |   |-------|   OK       |-------|   |   OK        |--|-----|   NO!
##  r=0                                  r=0              r=0
#@end group 
#@end example
## 
## The equation taken into account is:
##
## - 1/r * d/dr (@var{alpha} * @var{gamma} (@var{eta} du/dr - @var{beta} u)) = f
##
## where @var{alpha} is an element-wise constant scalar function,
## @var{eta} and @var{gamma} are piecewise linear conforming scalar
## functions, @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain. 
##
## @seealso{bim1a_axisymmetric_rhs, bim1a_axisymmetric_reaction, 
## bim1a_axisymmetric_laplacian, bim2a_axisymmetric_advection_diffusion} 
## @end deftypefn

function A = bim1a_axisymmetric_advection_diffusion (x,alpha,gamma,eta,beta)

  ## Check input
  if nargin != 5
    error("bim1a_axisymmetric_advection_diffusion: wrong number of input parameters.");
  elseif !isvector(x)
    error("bim1a_axisymmetric_advection_diffusion: first argument is not a valid vector.");
  endif

  nnodes = length(x);
  nelem  = nnodes-1;

  ## Turn scalar input to a vector of appropriate size
  if isscalar(alpha)
    alpha = alpha*ones(nelem,1);
  endif
  if isscalar(gamma)
    gamma = gamma*ones(nnodes,1);
  endif
  if isscalar(eta)
    eta = eta*ones(nnodes,1);
  endif
  
  if !( isvector(alpha) && isvector(gamma) && isvector(eta) )
    error("bim1a_axisymmetric_advection_diffusion: coefficients are not valid vectors.");
  elseif (length(alpha) != nelem)
    error("bim1a_axisymmetric_advection_diffusion: length of alpha is not equal to the number of elements.");
  elseif (length(gamma) != nnodes)
    error("bim1a_axisymmetric_advection_diffusion: length of gamma is not equal to the number of nodes.");
  elseif (length(eta) != nnodes)
    error("bim1a_axisymmetric_advection_diffusion: length of eta is not equal to the number of nodes.");
  endif

  areak = reshape(diff(x),[],1);
  cm    = reshape((x(1:end-1)+x(2:end))/2,[],1);
  
  if (length(beta) == 1)
    vk = 0;
  elseif (length(beta) == nelem)
    vk = beta .* areak;
  elseif (length(beta) == nnodes)
    vk = diff(beta);
  else
    error("bim1a_axisymmetric_advection_diffusion: coefficient beta has wrong dimensions.");
  endif
  
  gammaetak = bimu_logm ( (gamma.*eta)(1:end-1), (gamma.*eta)(2:end));
  veta      = diff(eta);
  etak      = bimu_logm ( eta(1:end-1), eta(2:end));
  ck        = alpha .* gammaetak .* etak ./ areak .* abs(cm); 

  [bpk, bmk]  = bimu_bernoulli( (vk - veta)./etak);
 
  dm1 = [-(ck.*bmk); NaN]; 
  dp1 = [NaN; -(ck.*bpk)]; 
  d0  = [(ck(1).*bmk(1)); ((ck.*bmk)(2:end) + (ck.*bpk)(1:end-1)); (ck(end).*bpk(end))];
  A   = spdiags([dm1, d0, dp1],-1:1,nnodes,nnodes);

endfunction

%!test
%! n = 3;
%! mesh     = linspace(1,2,n+1)';
%! uex      = @(r) exp(r);
%! duexdr   = @(r) uex(r);
%! d2uexdr2 = @(r) uex(r);
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1; v = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*v*ones(Nelements,1);
%! f = @(r) -D./r.*duexdr(r) - D.*d2uexdr2(r) ...
%!         + v./r .* uex(r) + v * duexdr(r);
%! rhs    = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1); u([1,end]) = uex(mesh([1 end]));
%! u(2:end-1) = S(2:end-1,2:end-1)\(rhs(2:end-1) - S(2:end-1,[1 end])*u([1 end]));
%! assert(u,uex(mesh),1e-7)

%!test
%! n = 100;
%! mesh      = linspace(0,1,n+1)';
%! cm        = (mesh(1:end-1) + mesh(2:end))/2; 
%! uex       = @(r) - r.^2 + 1;
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1;  v = 0;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = v;
%! f      = @(r) 4*D;
%! rhs    = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)

%!test
%! n = 100;
%! mesh      = linspace(0,1,n+1)';
%! cm        = (mesh(1:end-1) + mesh(2:end))/2; 
%! uex       = @(r) - r.^2 + 1;
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1;  v = cm;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*v;
%! f      = @(r) 4*D + 2 - 4*r.^2;
%! rhs    = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)

%!test
%! x = linspace(0,1,101);
%! A = bim1a_axisymmetric_advection_diffusion(x,1,1,1,0);
%! alpha = ones(100,1);
%! gamma = ones(101,1);
%! eta   = gamma;
%! B = bim1a_axisymmetric_advection_diffusion(x,alpha,gamma,eta,0);
%! assert(A,B)
bim-1.1.8/inst/bim1a_axisymmetric_advection_upwind.m000066400000000000000000000065721502773057700226630ustar00rootroot00000000000000## Copyright (C) 2010-2014  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = bim1a_axisymmetric_advection_upwind (@var{mesh}, @var{beta})
##
## Build the Upwind stabilized stiffness matrix for an advection problem 
## in cylindrical coordinates with axisymmetric configuration.
## 
## The equation taken into account is:
##
## 1/r * (r * @var{beta} u)' = f
##
## where @var{beta} is an element-wise constant.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain. 
##
## @seealso{bim1a_axisymmetric_advection_diffusion, bim1a_axisymmetric_rhs,
## bim1a_axisymmetric_reaction, bim1a_axisymmetric_laplacian}
## @end deftypefn

function A = bim1a_axisymmetric_advection_upwind (x, beta)

  ## Check input
  if nargin != 2
    error("bim1a_axisymmetric_advection_upwind: wrong number of input parameters.");
  endif
  
  nnodes = length(x);
  nelem  = nnodes-1;

  cm    = reshape((x(1:end-1)+x(2:end))/2,[],1);
  
  if (length(beta) == 1)
    vk = 0;#zeros(nelem,1);
  elseif (length(beta) == nelem)
    vk = beta; 
  elseif (length(beta) == nnodes)
    vk = diff(beta);
  else
    error("bim1a_axisymmetric_advection_upwind: coefficient beta has wrong dimensions.");
  endif

  bmk =  (vk+abs(vk))/2 .* abs(cm);
  bpk = -(vk-abs(vk))/2 .* abs(cm);
 
  dm1 = [-bmk; NaN]; 
  dp1 = [NaN; -bpk]; 
  d0  = [bmk(1); bmk(2:end) + bpk(1:end-1); bpk(end)];
  A   = spdiags([dm1, d0, dp1],-1:1,nnodes,nnodes);

endfunction

%!test
%! nn = 20;
%! mesh = linspace(1,2,nn+1)';
%! D = 1;  v = 0;  sigma = 0;
%! uex      = @(r) exp(r);
%! duexdr   = @(r) uex(r);
%! d2uexdr2 = @(r) uex(r);
%! f = @(r,z) -D./r.*duexdr(r) - D.*d2uexdr2(r) ...
%!           + v./r .* uex(r) + v * duexdr(r) ...
%!           + sigma * uex(r);
%! uex_left = uex(mesh(1));  uex_right = uex(mesh(end));
%! Ar  = bim1a_axisymmetric_laplacian (mesh, D, 1);
%! Adv = bim1a_axisymmetric_advection_upwind (mesh, v*ones(nn,1));
%! R   = bim1a_axisymmetric_reaction (mesh, sigma, 1);
%! M = Ar + Adv + R;
%! M(1,:)   *= 0;  M(1,1) = 1;
%! M(end,:) *= 0;  M(end, end)  = 1;
%! rhs = bim1a_axisymmetric_rhs (mesh, 1, f(mesh));
%! rhs(1)   = uex_left;  rhs(end) = uex_right;
%! uh = M \ rhs;  
%! assert(uh, uex(mesh), 1e-3);
bim-1.1.8/inst/bim1a_axisymmetric_laplacian.m000066400000000000000000000047011502773057700212350ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo Porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{A}} = bim1a_axisymmetric_laplacian (@var{mesh},@var{epsilon},@var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration. 
## Rotational symmetry is assumed with respect to be the vertical
## axis r=0. Only grids that DO NOT contain r=0 are admissible.
##
##@example
##@group
##   |   |-------|   OK       |--|-----|   NO!
##  r=0                         r=0
#@end group 
#@end example
##
## The equation taken into account is:
##
## - 1/r * (r * @var{epsilon} * @var{kappa} ( u' ))' = f
## 
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim1a_axisymmetric_rhs, bim1a_axisymmetric_reaction, 
## bim1a_axisymmetric_advection_diffusion, bim2a_laplacian, bim3a_laplacian}
## @end deftypefn

function [A] = bim1a_axisymmetric_laplacian(mesh,epsilon,kappa)
  
  ## Check input
  if nargin != 3
    error("bim1a_axisymmetric_laplacian: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_axisymmetric_laplacian: first argument is not a valid vector.");
  endif

  ## Input-type check inside bim1a_axisymmetric_advection_diffusion
  nnodes = length(mesh);
  nelem  = nnodes - 1;
  
  A = bim1a_axisymmetric_advection_diffusion (mesh, epsilon, kappa, ones(nnodes,1), 0);
  
endfunction
bim-1.1.8/inst/bim1a_axisymmetric_reaction.m000066400000000000000000000107271502773057700211220ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo Porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{C}]} = @
## bim1a_axisymmetric_reaction(@var{mesh},@var{delta},@var{zeta})
##
## Build the lumped finite element mass matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration. 
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
## 
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim1a_axisymmetric_rhs, bim1a_axisymmetric_advection_diffusion, bim1a_axisymmetric_laplacian,
## bim2a_reaction, bim3a_reaction}
## @end deftypefn

function [C] = bim1a_axisymmetric_reaction(mesh,delta,zeta)
  
  ## Check input
  if nargin != 3
    error("bim1a_axisymmetric_reaction: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_axisymmetric_reaction: first argument is not a valid vector.");
  endif

  mesh    = reshape(mesh,[],1);
  nnodes  = length(mesh);
  nelems  = nnodes-1;

  ## Turn scalar input to a vector of appropriate size
  if isscalar(delta)
    delta = delta*ones(nelems,1);
  endif
  if isscalar(zeta)
    zeta  = zeta*ones(nnodes,1);
  endif

  if !( isvector(delta) && isvector(zeta) )
    error("bim1a_axisymmetric_reaction: coefficients are not valid vectors.");
  elseif length(delta) != nelems
    error("bim1a_axisymmetric_reaction: length of delta is not equal to the number of elements.");
  elseif length(zeta)  != nnodes
    error("bim1a_axisymmetric_reaction: length of zeta is not equal to the number of nodes.");
  endif

  h 	= (mesh(2:end)-mesh(1:end-1)).*delta;
  d0	= zeta.*[h(1)/2; (h(1:end-1)+h(2:end))/2; h(end)/2];
  C   = spdiags(d0.*abs(mesh), 0, nnodes,nnodes);

endfunction

%!test
%! n = 100;
%! mesh      = linspace(0,1,n+1)';
%! cm        = (mesh(1:end-1) + mesh(2:end))/2; 
%! uex       = @(r) - r.^2 + 1;
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1;  v = cm;  sigma = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 0;
%! delta  = ones(Nelements,1);
%! zeta   = sigma*ones(Nnodes,1);
%! f      = @(r) 4*D + sigma*uex(r);
%! rhs    = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! R = bim1a_axisymmetric_reaction(mesh, delta, zeta);
%! S += R;
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)

%!test
%! n = 100;
%! mesh      = linspace(0,1,n+1)';
%! cm        = (mesh(1:end-1) + mesh(2:end))/2; 
%! uex       = @(r) - r.^2 + 1;
%! Nnodes    = numel(mesh);
%! Nelements = Nnodes-1;
%! D = 1;  v = cm;  sigma = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*v;
%! delta  = ones(Nelements,1);
%! zeta   = sigma*ones(Nnodes,1);
%! f      = @(r) 4*D + 2 - 4*r.^2 + sigma*uex(r);
%! rhs    = bim1a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh));
%! S = bim1a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! R = bim1a_axisymmetric_reaction(mesh, delta, zeta);
%! S += R;
%! u = zeros(Nnodes,1); u(end) = uex(mesh(end));
%! u(1:end-1) = S(1:end-1,1:end-1)\(rhs(1:end-1) - S(1:end-1,end)*u(end));
%! assert(u,uex(mesh),1e-3)

%!test
%! x = linspace(0,1,101);
%! A = bim1a_axisymmetric_reaction(x,1,1);
%! delta = ones(100,1);
%! zeta  = ones(101,1);
%! B = bim1a_axisymmetric_reaction(x,delta,zeta);
%! assert(A,B)
bim-1.1.8/inst/bim1a_axisymmetric_rhs.m000066400000000000000000000052261502773057700201100ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo Porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = @
## bim1a_rhs(@var{mesh},@var{f}, @var{g}) 
##
## Build the finite element right-hand side of a diffusion problem
## employing mass-lumping.
##
## The equation taken into account is:
##
## @var{delta} * u = f * g
## 
## where @var{f} is an element-wise constant scalar function, while
## @var{g} is a piecewise linear conforming scalar function.
## 
## @seealso{bim1a_reaction, bim1a_advection_diffusion, bim1a_laplacian,
## bim2a_reaction, bim3a_reaction}
## @end deftypefn

function b = bim1a_axisymmetric_rhs(mesh,f,g)

  ## Check input
  if nargin != 3
    error("bim1a_rad_rhs: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_rad_rhs: first argument is not a valid vector.");
  endif

  mesh   = reshape(mesh,[],1);
  nnodes = length(mesh);
  nelem  = nnodes-1;

  ## Turn scalar input to a vector of appropriate size
  if isscalar(f)
    f = f*ones(nelem,1);
  endif
  if isscalar(g)
    g = g*ones(nnodes,1);
  endif

  if !( isvector(f) && isvector(g) )
    error("bim1a_rad_rhs: coefficients are not valid vectors.");
  elseif (length(f) != nelem && length(f) != 1)
    error("bim1a_rad_rhs: length of f is not equal to the number of elements.");
  elseif (length(g) != nnodes && length(g) != 1)
    error("bim1a_rad_rhs: length of g is not equal to the number of nodes.");
  endif

  h = (mesh(2:end)-mesh(1:end-1)).*f;
  b = g.*[h(1)/2; (h(1:end-1)+h(2:end))/2; h(end)/2] .* abs(mesh);

endfunction

%!test
%! x = linspace(0,1,101);
%! A = bim1a_axisymmetric_rhs(x,1,1);
%! delta = ones(100,1);
%! zeta  = ones(101,1);
%! B = bim1a_axisymmetric_rhs(x,delta,zeta);
%! assert(A,B)
bim-1.1.8/inst/bim1a_laplacian.m000066400000000000000000000036321502773057700164410ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{A}} = bim1a_laplacian (@var{mesh},@var{epsilon},@var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## - (@var{epsilon} * @var{kappa} ( u' ))' = f
## 
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim1a_rhs, bim1a_reaction, bim1a_advection_diffusion,
## bim2a_laplacian, bim3a_laplacian}
## @end deftypefn

function [A] = bim1a_laplacian(mesh,epsilon,kappa)
  
  ## Check input
  if nargin != 3
    error("bim1a_laplacian: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_laplacian: first argument is not a valid vector.");
  endif

  ## Input-type check inside bim1a_advection_diffusion
  nnodes = numel (mesh);
  nelem  = nnodes - 1;
  
  A = bim1a_advection_diffusion (mesh, epsilon, kappa, ones(nnodes,1), 0);
  
endfunction
bim-1.1.8/inst/bim1a_reaction.m000066400000000000000000000051371502773057700163230ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{C}]} = @
## bim1a_reaction(@var{mesh},@var{delta},@var{zeta})
##
## Build the lumped finite element mass matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
## 
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim1a_rhs, bim1a_advection_diffusion, bim1a_laplacian,
## bim2a_reaction, bim3a_reaction}
## @end deftypefn

function [C] = bim1a_reaction(mesh,delta,zeta)
  
  ## Check input
  if nargin != 3
    error("bim1a_reaction: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_reaction: first argument is not a valid vector.");
  endif

  mesh    = reshape (mesh, [], 1);
  nnodes  = numel (mesh);
  nelems  = nnodes - 1;

  ## Turn scalar input to a vector of appropriate size
  if isscalar(delta)
    delta  = delta*ones(nelems,1);
  endif
  if isscalar(zeta)
    zeta  = zeta*ones(nnodes,1);
  endif

  if !( isvector(delta) && isvector(zeta) )
    error("bim1a_reaction: coefficients are not valid vectors.");
  elseif numel (delta) != nelems
    error("bim1a_reaction: length of delta is not equal to the number of elements.");
  elseif numel (zeta)  != nnodes
    error("bim1a_reaction: length of zeta is not equal to the number of nodes.");
  endif

  h 	= (mesh(2:end)-mesh(1:end-1)).*delta;
  d0	= zeta.*[h(1)/2; (h(1:end-1)+h(2:end))/2; h(end)/2];
  C     = spdiags(d0, 0, nnodes,nnodes);

endfunction

%!test
%! x = linspace(0,1,101);
%! A = bim1a_reaction(x,1,1);
%! delta = ones(100,1);
%! zeta  = ones(101,1);
%! B = bim1a_reaction(x,delta,zeta);
%! assert(A,B)
bim-1.1.8/inst/bim1a_rhs.m000066400000000000000000000047511502773057700153140ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = @
## bim1a_rhs(@var{mesh},@var{f}, @var{g}) 
##
## Build the finite element right-hand side of a diffusion problem
## employing mass-lumping.
##
## The equation taken into account is:
##
## @var{delta} * u = f * g
## 
## where @var{f} is an element-wise constant scalar function, while
## @var{g} is a piecewise linear conforming scalar function.
## 
## @seealso{bim1a_reaction, bim1a_advection_diffusion, bim1a_laplacian,
## bim2a_reaction, bim3a_reaction}
## @end deftypefn

function b = bim1a_rhs(mesh,f,g)

  ## Check input
  if nargin != 3
    error("bim1a_rhs: wrong number of input parameters.");
  elseif !isvector(mesh)
    error("bim1a_rhs: first argument is not a valid vector.");
  endif

  mesh   = reshape(mesh,[],1);
  nnodes = numel (mesh);
  nelem  = nnodes-1;

  ## Turn scalar input to a vector of appropriate size
  if isscalar(f)
    f = f*ones(nelem,1);
  endif
  if isscalar(g)
    g = g*ones(nnodes,1);
  endif

  if !( isvector(f) && isvector(g) )
    error("bim1a_rhs: coefficients are not valid vectors.");
  elseif (numel (f) != nelem && numel (f) != 1)
    error("bim1a_rhs: length of f is not equal to the number of elements.");
  elseif (numel (g) != nnodes && numel (g) != 1)
    error("bim1a_rhs: length of g is not equal to the number of nodes.");
  endif

  h = (mesh(2:end)-mesh(1:end-1)).*f;
  b = g.*[h(1)/2; (h(1:end-1)+h(2:end))/2; h(end)/2];

endfunction

%!test
%! x = linspace(0,1,101);
%! A = bim1a_rhs(x,1,1);
%! delta = ones(100,1);
%! zeta  = ones(101,1);
%! B = bim1a_rhs(x,delta,zeta);
%! assert(A,B)
bim-1.1.8/inst/bim1c_elem_to_nodes.m000066400000000000000000000054121502773057700173310ustar00rootroot00000000000000## Copyright (C) 2013 Carlo de Falco
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## .

## -*- texinfo -*-
##
## @deftypefn {Function File} {@var{u_nod}} = bim1c_elem_to_nodes (@var{mesh}, @var{u_el}) 
## @deftypefnx {Function File} {@var{u_nod}} = bim1c_elem_to_nodes (@var{m_el}, @var{u_el}) 
## @deftypefnx {Function File} {[@var{u_nod}, @var{m_el}]} = bim1c_elem_to_nodes ( ... ) 
##
## Compute interpolated values at nodes @var{u_nod} given values at element mid-points @var{u_el}.
## If called with more than one output, also return the interpolation matrix @var{m_el} such that
## @code{u_nod = m_el * u_el}.
## If repeatedly performing interpolation on the same mesh the matrix @var{m_el} obtained by a previous call 
## to @code{bim1c_elem_to_nodes} may be passed as input to avoid unnecessary computations.
##
## @end deftypefn


## Author: Carlo de Falco 
## Author: Matteo Porro 
## Created: 2013-11-04

function [u_nod, m_el] = bim1c_elem_to_nodes (m, u_el)

  if (nargout > 1 )
    if (isvector (m))
      nel  = numel (m) - 1;
      nnod = numel (m);
      m_el = spalloc (nnod, nel, 2 * nel);
      h = diff (m);
      for iel = 1:nel
        m_el([iel, iel+1], iel) = h(iel);
      endfor
      m_el = diag (sum (m_el, 2)) \ m_el;
    elseif (ismatrix (m))
      m_el = m;
    else
      error (["bim1c_elem_to_nodes: first input ", ...
              "parameter is of incorrect type"]);
    endif
    u_nod = m_el * u_el;
  else
    if (isvector (m))
      rhs  = bim1a_rhs (m, u_el, 1);
      mass = bim1a_reaction (m, 1, 1);
      u_nod = full (mass \ rhs);
    elseif (ismatrix (m))
      u_nod = m * u_el;
    else
      error (["bim1c_elem_to_nodes: first input ", ...
              "parameter is of incorrect type"]);
    endif      
  endif

endfunction

%!test
%! n = 10; msh = linspace (0, 1, n+1);
%! nel  = n;
%! nnod = n+1;
%! u_el = randn (nel, 1);
%! un1 = bim1c_elem_to_nodes (msh, u_el);
%! [un2, m] = bim1c_elem_to_nodes (msh, u_el);
%! un3 = bim1c_elem_to_nodes (m, u_el);
%! [un4, m] = bim1c_elem_to_nodes (m, u_el);
%! assert (un1, un2, 1e-10)
%! assert (un1, un3, 1e-10)
%! assert (un1, un4, 1e-10)

bim-1.1.8/inst/bim1c_norm.m000066400000000000000000000072321502773057700154720ustar00rootroot00000000000000## Copyright (C) 2006-2013  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Matteo Porro       

## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{norm_u}]} = @
## bim1c_norm(@var{mesh},@var{u},@var{norm_type}) 
##
## Compute the @var{norm_type}-norm of function @var{u} on the domain described
## by the triangular grid @var{mesh}.
##
## The input function @var{u} can be either a piecewise linear conforming scalar
## function or an elementwise constant scalar or vector function.
##
## The string parameter @var{norm_type} can be one among 'L2', 'H1' and 'inf'.
##
## Should the input function be piecewise constant, the H1 norm will not be 
## computed and the function will return an error message.
##
## @seealso{bim2c_norm, bim3c_norm}
##
## @end deftypefn

function [norm_u] = bim1c_norm (m, u, norm_type)

  ## Check input  
  if (nargin != 3)
    error ("bim1c_norm: wrong number of input parameters.");
  elseif (! isvector (m))
    error ("bim1c_norm: first input is not a valid mesh.");
  endif

  nnodes = numel (m);
  nel    = numel (m) - 1;
  
  if (isrow (u))
    u = u';
  endif
  if (isrow (m))
    m = m';
  endif

  if ((numel (u) != nnodes) && (numel (u) != nel))
    error ("bim1c_norm: numel(u) != nnodes and numel(u) != nel.");
  endif
  
  if (! (strcmp (norm_type, 'L2') 
         || strcmp (norm_type, 'inf') 
         || strcmp (norm_type, 'H1')))
    error ("bim1c_norm: invalid norm type parameter.");
  endif

  if (strcmp (norm_type,'inf'))  
    norm_u = max (abs (u));
  else
    if (numel (u) == nnodes)

      M = __mass_matrix__ (m);
      
      if (strcmp (norm_type, 'H1'))
        A = bim1a_laplacian (m, 1, 1);
        M += A;
      endif

      norm_u = sqrt(u' * M * u);
    
    else

      if (strcmp (norm_type, 'H1'))
        error (["bim1c_norm: cannot compute the ", ...
                "H1 norm of an elementwise constant function."]);
      endif
      
      norm_u = diff(m)' * u.^2;      
      norm_u = sqrt (norm_u);

    endif
  endif

endfunction

function M = __mass_matrix__ (m)
  
  nnodes = numel(m);
  
  h   = diff(m);
  d0  = 1/3*[h(1); h(1:end-1)+h(2:end); h(end)];
  d1  = [0; 1/6*h];
  dm1 = [1/6*h; 0];

  M  = spdiags([dm1 d0 d1], -1:1, nnodes, nnodes);
  
endfunction

%!test
%!shared L, V, m
%! L = rand (1); V = rand (1); m = linspace (0,1,5).^2;  m *= L;
%! u    = V * ones (size (m))';
%! uinf = bim1c_norm (m, u, 'inf');
%! uL2  = bim1c_norm (m, u, 'L2');
%! uH1  = bim1c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], [V, V*sqrt(L), V*sqrt(L)], sqrt(eps));
%!test
%! u    = V * m';
%! uinf = bim1c_norm (m, u, 'inf');
%! uL2  = bim1c_norm (m, u, 'L2');
%! uH1  = bim1c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], 
%!         [L*V, V*sqrt(L^3/3), V*sqrt(L^3/3 + L)],
%!          1e-12);
%!test
%! u    = V * ones (size (diff (m)))';
%! uinf = bim1c_norm (m, u, 'inf');
%! uL2  = bim1c_norm (m, u, 'L2');
%! assert ([uinf, uL2], [V, V*sqrt(L)], 1e-12);

bim-1.1.8/inst/bim2a_advection_diffusion.m000066400000000000000000000275211502773057700205430ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim2a_advection_diffusion(@var{mesh},@var{alpha},@var{gamma},@var{eta},@var{beta})
##
## Build the Scharfetter-Gummel stabilized stiffness matrix for a
## diffusion-advection problem. 
## 
## The equation taken into account is:
##
## - div (@var{alpha} * @var{gamma} (@var{eta} grad (u) - @var{beta} u )) = f
##
## where @var{alpha} is an element-wise constant scalar function,
## @var{eta} and @var{gamma} are piecewise linear conforming scalar
## functions, @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
## 
## Example:
## @example
## mesh = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
## mesh = bim2c_mesh_properties(mesh);
## x    = mesh.p(1,:)';
##
## Dnodes    = bim2c_unknowns_on_side(mesh,[2,4]);
## Nnodes    = columns(mesh.p);
## Nelements = columns(mesh.t);
## Varnodes  = setdiff(1:Nnodes,Dnodes);
##
## alpha  = ones(Nelements,1);
## eta    = .1*ones(Nnodes,1);
## beta   = [ones(1,Nelements);zeros(1,Nelements)];
## gamma  = ones(Nnodes,1);
## f      = bim2a_rhs(mesh,ones(Nnodes,1),ones(Nelements,1));
##
## S   = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
## u   = zeros(Nnodes,1);
## uex = x - (exp(10*x)-1)/(exp(10)-1);
## 
## u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
## 
## assert(u,uex,1e-7)
## @end example
##
## @seealso{bim2a_rhs, bim2a_reaction, bim2c_mesh_properties}
## @end deftypefn

function [A] = bim2a_advection_diffusion (mesh, alpha, gamma, eta, beta)

  ## Check input
  if nargin != 5
    error("bim2a_advection_diffusion: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_advection_diffusion: first input is not a valid mesh structure.");
  endif
  
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(alpha)
    alpha = alpha*ones(nelem,1);
  endif
  if isscalar(gamma)
    gamma = gamma*ones(nnodes,1);
  endif
  if isscalar(eta)
    eta = eta*ones(nnodes,1);
  endif

  if !( isvector(alpha) && isvector(gamma) && isvector(eta) )
    error("bim2a_advection_diffusion: coefficients are not valid vectors.");
  elseif (numel (alpha) != nelem)
    error("bim2a_advection_diffusion: length of alpha is not equal to the number of elements.");
  elseif (numel (gamma) != nnodes)
    error("bim2a_advection_diffusion: length of gamma is not equal to the number of nodes.");
  elseif (numel (eta) != nnodes)
    error("bim2a_advection_diffusion: length of eta is not equal to the number of nodes.");
  endif
  
  alphaareak = reshape (alpha.*mesh.area,1,1,nelem);
  shg        = mesh.shg(:,:,:);
  
  
  ## Build local Laplacian matrix	
  
  Lloc = zeros(3,3,nelem);	
  
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum( shg(:,inode,:) .* shg(:,jnode,:),1) .* alphaareak;
    endfor
  endfor
  
  x = mesh.p(1,:);
  x = x(mesh.t(1:3,:));
  y = mesh.p(2,:);
  y = y(mesh.t(1:3,:));
  
  if all(size(beta)==1)
    v12 = 0;
    v23 = 0;
    v31 = 0; 
  elseif all(size(beta)==[2,nelem])
    v12 = beta(1,:) .* (x(2,:)-x(1,:)) + beta(2,:) .* (y(2,:)-y(1,:));
    v23 = beta(1,:) .* (x(3,:)-x(2,:)) + beta(2,:) .* (y(3,:)-y(2,:));
    v31 = beta(1,:) .* (x(1,:)-x(3,:)) + beta(2,:) .* (y(1,:)-y(3,:)); 
  elseif all(size(beta)==[nnodes,1])
    betaloc = beta(mesh.t(1:3,:));
    v12     = betaloc(2,:)-betaloc(1,:);
    v23     = betaloc(3,:)-betaloc(2,:);
    v31     = betaloc(1,:)-betaloc(3,:); 
  else
    error("bim2a_advection_diffusion: coefficient beta has wrong dimensions.");
  endif
  
  etaloc = eta(mesh.t(1:3,:));
  
  eta12 = etaloc(2,:) - etaloc(1,:);
  eta23 = etaloc(3,:) - etaloc(2,:);
  eta31 = etaloc(1,:) - etaloc(3,:);
  
  etalocm1 = bimu_logm(etaloc(2,:),etaloc(3,:));
  etalocm2 = bimu_logm(etaloc(3,:),etaloc(1,:));
  etalocm3 = bimu_logm(etaloc(1,:),etaloc(2,:));
  
  gammaloc = gamma(mesh.t(1:3,:));
  geloc    = gammaloc.*etaloc;
  
  gelocm1 = bimu_logm (geloc(2,:), geloc(3,:));
  gelocm2 = bimu_logm (geloc(3,:), geloc(1,:));
  gelocm3 = bimu_logm (geloc(1,:), geloc(2,:));
  
  [bp12,bm12] = bimu_bernoulli ((v12 - eta12) ./ etalocm3);
  [bp23,bm23] = bimu_bernoulli ((v23 - eta23) ./ etalocm1);
  [bp31,bm31] = bimu_bernoulli ((v31 - eta31) ./ etalocm2);
  
  bp12 = reshape(gelocm3.*etalocm3.*bp12,1,1,nelem).*Lloc(1,2,:);
  bm12 = reshape(gelocm3.*etalocm3.*bm12,1,1,nelem).*Lloc(1,2,:);
  bp23 = reshape(gelocm1.*etalocm1.*bp23,1,1,nelem).*Lloc(2,3,:);
  bm23 = reshape(gelocm1.*etalocm1.*bm23,1,1,nelem).*Lloc(2,3,:);
  bp31 = reshape(gelocm2.*etalocm2.*bp31,1,1,nelem).*Lloc(3,1,:);
  bm31 = reshape(gelocm2.*etalocm2.*bm31,1,1,nelem).*Lloc(3,1,:);
  
  Sloc(1,1,:) = (-bm12-bp31)./reshape(etaloc(1,:),1,1,nelem);
  Sloc(1,2,:) = bp12./reshape(etaloc(2,:),1,1,nelem);
  Sloc(1,3,:) = bm31./reshape(etaloc(3,:),1,1,nelem);
  
  Sloc(2,1,:) = bm12./reshape(etaloc(1,:),1,1,nelem);
  Sloc(2,2,:) = (-bp12-bm23)./reshape(etaloc(2,:),1,1,nelem); 
  Sloc(2,3,:) = bp23./reshape(etaloc(3,:),1,1,nelem);
  
  Sloc(3,1,:) = bp31./reshape(etaloc(1,:),1,1,nelem);
  Sloc(3,2,:) = bm23./reshape(etaloc(2,:),1,1,nelem);
  Sloc(3,3,:) = (-bm31-bp23)./reshape(etaloc(3,:),1,1,nelem);
  
  A = sparse(ginode(:),gjnode(:),Sloc(:));


endfunction

%!test 
%! [mesh] = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x      = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! alpha  = ones(Nelements,1);
%! eta    = .1*ones(Nnodes,1);
%! beta   = [ones(1,Nelements);zeros(1,Nelements)];
%! gamma  = ones(Nnodes,1);
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ones(Nnodes,1));
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - (exp(10*x)-1)/(exp(10)-1);
%! assert(u,uex,1e-7)

%!test 
%! [mesh] = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x      = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = ones(Nelements,1);
%! eta    = .1*ones(Nnodes,1);
%! beta   = x;
%! gamma  = ones(Nnodes,1);
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ones(Nnodes,1));
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - (exp(10*x)-1)/(exp(10)-1);
%! assert(u,uex,1e-7)

%!test
%! [mesh] = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x      = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = 10*ones(Nelements,1);
%! eta    = .01*ones(Nnodes,1);
%! beta   = x/10;
%! gamma  = ones(Nnodes,1);
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ones(Nnodes,1));
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - (exp(10*x)-1)/(exp(10)-1);
%! assert(u,uex,1e-7)

%!test
%! [mesh] = msh2m_structured_mesh([0:1/3:1],[0:1/3:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x      = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = 10*ones(Nelements,1); eta = .001*ones(Nnodes,1);
%! beta   = x/100;
%! gamma  = 10*ones(Nnodes,1);
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ones(Nnodes,1));
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - (exp(10*x)-1)/(exp(10)-1);
%! assert(u,uex,1e-7)

%!test
%! [mesh] = msh2m_structured_mesh([0:1/1e3:1],[0:1/2:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x      = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = 3*ones(Nelements,1); eta = x+1;
%! beta   = [ones(1,Nelements);zeros(1,Nelements)];
%! gamma  = 2*x;
%! ff     = 2*(6*x.^2+6*x) - (6*x+6).*(1-2*x)+6*(x-x.^2);
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ff);
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - x.^2;
%! assert(u,uex,5e-3)

%!test
%! [mesh] = msh2m_structured_mesh([0:1/1e3:1],[0:1/2:1],1,1:4);
%! mesh = bim2c_mesh_properties(mesh);
%! x = mesh.p(1,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = ones(Nelements,1); eta = ones(Nnodes,1);
%! beta   = 0;
%! gamma  = x+1;
%! ff     = 4*x+1;
%! f      = bim2a_rhs(mesh,ones(Nelements,1),ff);
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x - x.^2; 
%! assert(u,uex,1e-7)

%!test
%! [mesh] = msh2m_structured_mesh([0:.1:1],[0:.1:1],1,1:4);
%! mesh = bim2c_mesh_properties(mesh);
%! x = mesh.p(1,:)';y = mesh.p(2,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[1:4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! Varnodes = setdiff(1:Nnodes,Dnodes);
%! alpha  = ones(Nelements,1); diff = 1e-2; eta=diff*ones(Nnodes,1);
%! beta   =[ones(1,Nelements);ones(1,Nelements)];
%! gamma  = x*0+1;
%! ux  = y.*(1-exp((y-1)/diff)) .* (1-exp((x-1)/diff)-x.*exp((x-1)/diff)/diff);
%! uy  = x.*(1-exp((x-1)/diff)) .* (1-exp((y-1)/diff)-y.*exp((y-1)/diff)/diff);
%! uxx = y.*(1-exp((y-1)/diff)) .* (-2*exp((x-1)/diff)/diff-x.*exp((x-1)/diff)/(diff^2));
%! uyy = x.*(1-exp((x-1)/diff)) .* (-2*exp((y-1)/diff)/diff-y.*exp((y-1)/diff)/(diff^2));
%! ff  = -diff*(uxx+uyy)+ux+uy;
%! f   = bim2a_rhs(mesh,ones(Nelements,1),ff);
%! S = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u = zeros(Nnodes,1);
%! u(Varnodes) = S(Varnodes,Varnodes)\f(Varnodes);
%! uex = x.*y.*(1-exp((x-1)/diff)).*(1-exp((y-1)/diff)); 
%! assert(u,uex,1e-7)

%!test
%! [mesh] = msh2m_structured_mesh([0:.1:1],[0:.1:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x = mesh.p(1,:)'; y = mesh.p(2,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[1:4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! alpha  = ones(Nelements,1); eta=ones(Nnodes,1);
%! beta   = 0;
%! gamma  = ones(Nnodes,1);
%! A = bim2a_advection_diffusion(mesh,1,1,1,0);
%! B = bim2a_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! assert(A,B)
bim-1.1.8/inst/bim2a_advection_upwind.m000066400000000000000000000075321502773057700200630ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim2a_advection_upwind (@var{mesh}, @var{beta})
##
## Build the UW stabilized stiffness matrix for an advection problem. 
## 
## The equation taken into account is:
##
## div (@var{beta} u) = f
##
## where @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
## 
## @seealso{bim2a_rhs, bim2a_reaction, bim2c_mesh_properties}
## @end deftypefn

function A = bim2a_advection_upwind (mesh, beta)

  ## Check input
  if nargin != 2
    error("bim2a_advection_upwind: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_advection_upwind: first input is not a valid mesh structure.");
  endif
  
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);
  
  alphaareak = reshape (mesh.area, 1, 1, nelem);
  shg        = mesh.shg(:,:,:);
  
  ## Build local Laplacian matrix	
  Lloc = zeros(3,3,nelem);	
  
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum( shg(:,inode,:) .* shg(:,jnode,:),1) .* alphaareak;
    endfor
  endfor
  
  x = mesh.p(1,:);
  x = x(mesh.t(1:3,:));
  y = mesh.p(2,:);
  y = y(mesh.t(1:3,:));
  
  if all(size(beta)==1)
    v12 = 0;
    v23 = 0;
    v31 = 0; 
  elseif all(size(beta)==[2,nelem])
    v12 = beta(1,:) .* (x(2,:)-x(1,:)) + beta(2,:) .* (y(2,:)-y(1,:));
    v23 = beta(1,:) .* (x(3,:)-x(2,:)) + beta(2,:) .* (y(3,:)-y(2,:));
    v31 = beta(1,:) .* (x(1,:)-x(3,:)) + beta(2,:) .* (y(1,:)-y(3,:)); 
  elseif all(size(beta)==[nnodes,1])
    betaloc = beta(mesh.t(1:3,:));
    v12     = betaloc(2,:)-betaloc(1,:);
    v23     = betaloc(3,:)-betaloc(2,:);
    v31     = betaloc(1,:)-betaloc(3,:); 
  else
    error("bim2a_advection_upwind: coefficient beta has wrong dimensions.");
  endif
  
  [bp12, bm12] = deal (- (v12 - abs (v12))/2, (v12 + abs (v12))/2);
  [bp23, bm23] = deal (- (v23 - abs (v23))/2, (v23 + abs (v23))/2);
  [bp31, bm31] = deal (- (v31 - abs (v31))/2, (v31 + abs (v31))/2);
  
  bp12 = reshape(bp12,1,1,nelem).*Lloc(1,2,:);
  bm12 = reshape(bm12,1,1,nelem).*Lloc(1,2,:);
  bp23 = reshape(bp23,1,1,nelem).*Lloc(2,3,:);
  bm23 = reshape(bm23,1,1,nelem).*Lloc(2,3,:);
  bp31 = reshape(bp31,1,1,nelem).*Lloc(3,1,:);
  bm31 = reshape(bm31,1,1,nelem).*Lloc(3,1,:);
  
  Sloc(1,1,:) = (-bm12-bp31);
  Sloc(1,2,:) = bp12;
  Sloc(1,3,:) = bm31;
  
  Sloc(2,1,:) = bm12;
  Sloc(2,2,:) = (-bp12-bm23); 
  Sloc(2,3,:) = bp23;
  
  Sloc(3,1,:) = bp31;
  Sloc(3,2,:) = bm23;
  Sloc(3,3,:) = (-bm31-bp23);
  
  A = sparse(ginode(:), gjnode(:), Sloc(:));


endfunction
bim-1.1.8/inst/bim2a_axisymmetric_advection_diffusion.m000066400000000000000000000340661502773057700233430ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim2a_axisymmetric_advection_diffusion(@var{mesh},@var{alpha},@var{gamma},@var{eta},@var{beta})
##
## Build the Scharfetter-Gummel stabilized stiffness matrix for a
## diffusion-advection problem in cylindrical coordinates with axisymmetric 
## configuration. Rotational symmetry is assumed with respect to be the vertical
## axis r=0. Only plane geometries that DO NOT intersect the symmetry axis 
## are admitted.
##
##@example
##@group
##    |   ____                 _|____ 
##    |  |    \               \ |    |
##  z |  |     \  OK           \|    |   NO!
##    |  |______\               |\___|
##    |     r                   |
#@end group 
#@end example
##
## The equation taken into account is:
##
## 1/r * d(r * Fr)/dr + dFz/dz = f
##
## with
##
## F = [Fr, Fz]' = - @var{alpha} * @var{gamma} ( @var{eta} grad (u) - @var{beta} u )
##
## where @var{alpha} is an element-wise constant scalar function,
## @var{eta} and @var{gamma} are piecewise linear conforming scalar
## functions, @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly, one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input. In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
##
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction, 
## bim2a_advection_diffusion, bim2c_mesh_properties}
## @end deftypefn

function [A] = bim2a_axisymmetric_advection_diffusion (mesh, alpha, gamma, eta, beta)

  ## Check input
  if nargin != 5
    error("bim2a_axisymmetric_advection_diffusion: wrong number of input parameters.");
  elseif !(isstruct(mesh) && isfield(mesh,"p") &&
	         isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_axisymmetric_advection_diffusion: first input is not a valid mesh structure.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_advection_diffusion: the input mesh cannot intersect the rotation axis r=0.");
  endif
  
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(alpha)
    alpha = alpha*ones(nelem,1);
  endif
  if isscalar(gamma)
    gamma = gamma*ones(nnodes,1);
  endif
  if isscalar(eta)
    eta = eta*ones(nnodes,1);
  endif

  if !( isvector(alpha) && isvector(gamma) && isvector(eta) )
    error("bim2a_axisymmetric_advection_diffusion: coefficients are not valid vectors.");
  elseif length(alpha) != nelem
    error("bim2a_axisymmetric_advection_diffusion: length of alpha is not equal to the number of elements.");
  elseif length(gamma) != nnodes
    error("bim2a_axisymmetric_advection_diffusion: length of gamma is not equal to the number of nodes.");
  elseif length(eta) != nnodes
    error("bim2a_axisymmetric_advection_diffusion: length of eta is not equal to the number of nodes.");
  endif
  
  x = abs(mesh.p(1,:));
  x = x(mesh.t(1:3,:));
  y = mesh.p(2,:);
  y = y(mesh.t(1:3,:));
   
  alphaareak = reshape (alpha.*mesh.area,1,1,nelem);
  shg        = mesh.shg(:,:,:);
  
  ## Build local Laplacian matrix
  Lloc = zeros(3,3,nelem);	
  
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum( shg(:,inode,:) .* shg(:,jnode,:),1) .* alphaareak;
    endfor
  endfor
    
  if all(size(beta)==1)
    v12 = 0;
    v23 = 0;
    v31 = 0; 
  elseif all(size(beta)==[2,nelem])
    v12 = beta(1,:) .* (x(2,:)-x(1,:)) + beta(2,:) .* (y(2,:)-y(1,:));
    v23 = beta(1,:) .* (x(3,:)-x(2,:)) + beta(2,:) .* (y(3,:)-y(2,:));
    v31 = beta(1,:) .* (x(1,:)-x(3,:)) + beta(2,:) .* (y(1,:)-y(3,:)); 
  elseif all(size(beta)==[nnodes,1])
    betaloc = beta(mesh.t(1:3,:));
    v12     = betaloc(2,:)-betaloc(1,:);
    v23     = betaloc(3,:)-betaloc(2,:);
    v31     = betaloc(1,:)-betaloc(3,:); 
  else
    error("bim2a_axisymmetric_advection_diffusion: coefficient beta has wrong dimensions.");
  endif
  
  etaloc = eta(mesh.t(1:3,:));
  
  eta12 = etaloc(2,:) - etaloc(1,:);
  eta23 = etaloc(3,:) - etaloc(2,:);
  eta31 = etaloc(1,:) - etaloc(3,:);
  
  r12 = (x(2,:) + x(1,:)) / 2;
  r23 = (x(3,:) + x(2,:)) / 2;
  r31 = (x(1,:) + x(3,:)) / 2;
  
  etalocm1 = bimu_logm(etaloc(2,:),etaloc(3,:));
  etalocm2 = bimu_logm(etaloc(3,:),etaloc(1,:));
  etalocm3 = bimu_logm(etaloc(1,:),etaloc(2,:));
  
  gammaloc = gamma(mesh.t(1:3,:));
  geloc    = gammaloc.*etaloc;
  
  gelocm1 = bimu_logm (geloc(2,:), geloc(3,:));
  gelocm2 = bimu_logm (geloc(3,:), geloc(1,:));
  gelocm3 = bimu_logm (geloc(1,:), geloc(2,:));
  
  [bp12,bm12] = bimu_bernoulli ((v12 - eta12) ./ etalocm3);
  [bp23,bm23] = bimu_bernoulli ((v23 - eta23) ./ etalocm1);
  [bp31,bm31] = bimu_bernoulli ((v31 - eta31) ./ etalocm2);
  
  bp12 = reshape(r12.*gelocm3.*etalocm3.*bp12,1,1,nelem).*Lloc(1,2,:);
  bm12 = reshape(r12.*gelocm3.*etalocm3.*bm12,1,1,nelem).*Lloc(1,2,:);
  bp23 = reshape(r23.*gelocm1.*etalocm1.*bp23,1,1,nelem).*Lloc(2,3,:);
  bm23 = reshape(r23.*gelocm1.*etalocm1.*bm23,1,1,nelem).*Lloc(2,3,:);
  bp31 = reshape(r31.*gelocm2.*etalocm2.*bp31,1,1,nelem).*Lloc(3,1,:);
  bm31 = reshape(r31.*gelocm2.*etalocm2.*bm31,1,1,nelem).*Lloc(3,1,:);
  
  Sloc(1,1,:) = (-bm12-bp31)./reshape(etaloc(1,:),1,1,nelem);
  Sloc(1,2,:) = bp12./reshape(etaloc(2,:),1,1,nelem);
  Sloc(1,3,:) = bm31./reshape(etaloc(3,:),1,1,nelem);
  
  Sloc(2,1,:) = bm12./reshape(etaloc(1,:),1,1,nelem);
  Sloc(2,2,:) = (-bp12-bm23)./reshape(etaloc(2,:),1,1,nelem); 
  Sloc(2,3,:) = bp23./reshape(etaloc(3,:),1,1,nelem);
  
  Sloc(3,1,:) = bp31./reshape(etaloc(1,:),1,1,nelem);
  Sloc(3,2,:) = bm23./reshape(etaloc(2,:),1,1,nelem);
  Sloc(3,3,:) = (-bm31-bp23)./reshape(etaloc(3,:),1,1,nelem);
  
  A = sparse(ginode(:),gjnode(:),Sloc(:));

endfunction

%!test
%! n         = 3;
%! [mesh]    = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) 0*uex(r,z);
%! d2uexdz2  = @(r,z) 0*uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D = 1; vr = 1; vz = 0;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-7)

%!test
%! n         = 20;
%! [mesh]    = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r) .* exp(1-z);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) -uex(r,z);
%! d2uexdz2  = @(r,z) uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[1,2,3,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D = 1; vr = 1; vz = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-3)

%!test
%! n         = 10;
%! [mesh]    = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r) .* exp(1-z);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) -uex(r,z);
%! d2uexdz2  = @(r,z) uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[1,2,3,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D      = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D * mesh.p(1,:)';
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + 1./r .* uex(r,z) + duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-3)

%!test
%! n         = 10;
%! [mesh]    = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r) .* exp(1-z);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) -uex(r,z);
%! d2uexdz2  = @(r,z) uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[1,2,3,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D         = 1;
%! alpha     = D*ones(Nelements,1);
%! gamma     = ones(Nnodes,1);
%! eta       = ones(Nnodes,1);
%! beta      = 1/D * 1/2*(mesh.p(1,:)').^2;
%! f         = @(r,z) 1./r.*(1+r).*(r-D) .* uex(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-3)

%!test
%! n         = 3;
%! [mesh]    = msh2m_structured_mesh(linspace(-2,-1,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) 0*uex(r,z);
%! d2uexdz2  = @(r,z) 0*uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[2,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D = 1; vr = 1; vz = 0;
%! alpha     = D*ones(Nelements,1);
%! gamma     = ones(Nnodes,1);
%! eta       = ones(Nnodes,1);
%! beta      = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(abs(mesh.p(1,:)), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(abs(mesh.p(1,Dnodes)), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(abs(mesh.p(1,:)), mesh.p(2,:))',1e-7)

%!test
%! n         = 10;
%! [mesh]    = msh2m_structured_mesh(linspace(-2,-1,n+1),linspace(0,1,n+1),1,1:4);
%! mesh      = bim2c_mesh_properties(mesh);
%! uex       = @(r,z) exp(r) .* exp(1-z);
%! duexdr    = @(r,z) uex(r,z);
%! d2uexdr2  = @(r,z) uex(r,z);
%! duexdz    = @(r,z) -uex(r,z);
%! d2uexdz2  = @(r,z) uex(r,z);
%! Dnodes    = bim2c_unknowns_on_side(mesh,[1,2,3,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D         = 1;
%! alpha     = D*ones(Nelements,1);
%! gamma     = ones(Nnodes,1);
%! eta       = ones(Nnodes,1);
%! beta      = 1/D * 1/2*(mesh.p(1,:)').^2;
%! f         = @(r,z) 1./r.*(1+r).*(r-D) .* uex(r,z);
%! rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(abs(mesh.p(1,:)), mesh.p(2,:)));
%! S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! u   = zeros(Nnodes,1); u(Dnodes) = uex(abs(mesh.p(1,Dnodes)), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(abs(mesh.p(1,:)), mesh.p(2,:))',1e-3)

%!test
%! [mesh] = msh2m_structured_mesh([0:.1:1],[0:.1:1],1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! x = mesh.p(1,:)'; y = mesh.p(2,:)';
%! Dnodes = bim2c_unknowns_on_side(mesh,[1:4]);
%! Nnodes = columns(mesh.p); Nelements = columns(mesh.t);
%! alpha  = ones(Nelements,1); eta=ones(Nnodes,1);
%! beta   = 0;
%! gamma  = ones(Nnodes,1);
%! A = bim2a_axisymmetric_advection_diffusion(mesh,1,1,1,0);
%! B = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! assert(A,B)
bim-1.1.8/inst/bim2a_axisymmetric_advection_upwind.m000066400000000000000000000107601502773057700226560ustar00rootroot00000000000000## Copyright (C) 2006-2014 Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim2a_axisymmetric_advection_upwind (@var{mesh}, @var{beta})
##
## Build the Upwind stabilized stiffness matrix for an advection problem 
## in cylindrical coordinates with axisymmetric configuration.
## 
## The equation taken into account is:
##
## 1/r * d/dr (r * @var{beta}_r u) + d/dz (@var{beta}_z u) = f
##
## where @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
## 
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction, 
## bim2a_axisymmetric_advection_diffusion, bim2c_mesh_properties}
## @end deftypefn

function A = bim2a_axisymmetric_advection_upwind (mesh, beta)

  ## Check input
  if nargin != 2
    error("bim2a_axisymmetric_advection_upwind: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_axisymmetric_advection_upwind: first input is not a valid mesh structure.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_advection_upwind: the input mesh cannot intersect the rotation axis r=0.");
  endif

  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);
  
  x = abs (mesh.p(1,:));
  x = x(mesh.t(1:3,:));
  y = mesh.p(2,:);
  y = y(mesh.t(1:3,:));
  
  alphaareak = reshape (mesh.area, 1, 1, nelem);
  shg        = mesh.shg(:,:,:);
  
  ## Build local Laplacian matrix	
  Lloc = zeros(3,3,nelem);	
  
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum( shg(:,inode,:) .* shg(:,jnode,:),1) .* alphaareak;
    endfor
  endfor
  
  if all(size(beta)==1)
    v12 = 0;
    v23 = 0;
    v31 = 0; 
  elseif all(size(beta)==[2,nelem])
    v12 = beta(1,:) .* (x(2,:)-x(1,:)) + beta(2,:) .* (y(2,:)-y(1,:));
    v23 = beta(1,:) .* (x(3,:)-x(2,:)) + beta(2,:) .* (y(3,:)-y(2,:));
    v31 = beta(1,:) .* (x(1,:)-x(3,:)) + beta(2,:) .* (y(1,:)-y(3,:)); 
  elseif all(size(beta)==[nnodes,1])
    betaloc = beta(mesh.t(1:3,:));
    v12     = betaloc(2,:)-betaloc(1,:);
    v23     = betaloc(3,:)-betaloc(2,:);
    v31     = betaloc(1,:)-betaloc(3,:); 
  else
    error("bim2a_axisymmetric_advection_upwind: coefficient beta has wrong dimensions.");
  endif
  
  [bp12, bm12] = deal (- (v12 - abs (v12))/2, (v12 + abs (v12))/2);
  [bp23, bm23] = deal (- (v23 - abs (v23))/2, (v23 + abs (v23))/2);
  [bp31, bm31] = deal (- (v31 - abs (v31))/2, (v31 + abs (v31))/2);
  
  r12 = (x(2,:) + x(1,:)) / 2;
  r23 = (x(3,:) + x(2,:)) / 2;
  r31 = (x(1,:) + x(3,:)) / 2;

  bp12 = reshape(r12 .* bp12,1,1,nelem).*Lloc(1,2,:);
  bm12 = reshape(r12 .* bm12,1,1,nelem).*Lloc(1,2,:);
  bp23 = reshape(r23 .* bp23,1,1,nelem).*Lloc(2,3,:);
  bm23 = reshape(r23 .* bm23,1,1,nelem).*Lloc(2,3,:);
  bp31 = reshape(r31 .* bp31,1,1,nelem).*Lloc(3,1,:);
  bm31 = reshape(r31 .* bm31,1,1,nelem).*Lloc(3,1,:);
  
  Sloc(1,1,:) = (-bm12-bp31);
  Sloc(1,2,:) = bp12;
  Sloc(1,3,:) = bm31;
  
  Sloc(2,1,:) = bm12;
  Sloc(2,2,:) = (-bp12-bm23); 
  Sloc(2,3,:) = bp23;
  
  Sloc(3,1,:) = bp31;
  Sloc(3,2,:) = bm23;
  Sloc(3,3,:) = (-bm31-bp23);
  
  A = sparse(ginode(:), gjnode(:), Sloc(:));

endfunction
bim-1.1.8/inst/bim2a_axisymmetric_boundary_mass.m000066400000000000000000000144731502773057700221670ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{M}]} = @
## bim2a_axisymmetric_boundary_mass(@var{mesh},@var{sidelist},@var{nodelist})
##
## Build the lumped boundary mass matrix needed to apply Robin and Neumann
## boundary conditions in a problem in cylindrical coordinates with 
## axisymmetric configuration.
##
## The vector @var{sidelist} contains the list of the side edges
## contributing to the mass matrix.
##
## The optional argument @var{nodelist} contains the list of the
## degrees of freedom on the boundary.
##
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_advection_diffusion, 
## bim2a_axisymmetric_laplacian, bim2a_axisymmetric_reaction, bim2a_boundary_mass} 
## @end deftypefn

function [M] = bim2a_axisymmetric_boundary_mass(mesh,sidelist,nodelist)

  ## Check input
  if (nargin > 3)
    error ("bim2a_axisymmetric_boundary_mass: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	       isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_axisymmetric_boundary_mass: first input is not a valid mesh structure.");
  elseif !( isvector(sidelist) && isnumeric(sidelist) )
    error("bim2a_axisymmetric_boundary_mass: second input is not a valid numeric vector.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_boundary_mass: the input mesh cannot intersect the rotation axis r=0.");
  endif

  if (nargin < 3)
    [nodelist] = bim2c_unknowns_on_side(mesh,sidelist);
  endif

  r = abs (mesh.p(1,nodelist));

  edges = [];
  for ie = sidelist
    edges = [ edges, mesh.e([1:2 5],mesh.e(5,:)==ie)];
  endfor
  l  = sqrt((mesh.p(1,edges(1,:))-mesh.p(1,edges(2,:))).^2 +
	          (mesh.p(2,edges(1,:))-mesh.p(2,edges(2,:))).^2);
  
  dd = zeros(size(nodelist));
  
  for in = 1:length(nodelist)
    dd (in) = ( sum(r(in).*l(edges(1,:)==nodelist(in))) ...
              + sum(r(in).*l(edges(2,:)==nodelist(in))) )/2;
  endfor
  
  M = sparse(diag(dd));

endfunction

%!test
%! n = 3;
%! [mesh] = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! uex    = @(r,z) exp(r);
%! duexdr = @(r,z) uex(r,z);
%! d2uexdr2 = @(r,z) uex(r,z);
%! duexdz = @(r,z) 0*uex(r,z);
%! d2uexdz2 = @(r,z) 0*uex(r,z);
%! Rnodesr  = bim2c_unknowns_on_side(mesh,[2]);
%! Rnodesl  = bim2c_unknowns_on_side(mesh,[4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! D = 1; vr = 1; vz = 0;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
%! gr = @(r,z) uex(r,z) - 1 * (-D*duexdr(r,z) + vr*uex(r,z));
%! gl = @(r,z) uex(r,z) - (-1) * (-D*duexdr(r,z) + vr*uex(r,z));
%! rhs    = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! Mr = bim2a_axisymmetric_boundary_mass(mesh,2);  Ml = bim2a_axisymmetric_boundary_mass(mesh,4);
%! S(Rnodesr,Rnodesr) += Mr;
%! rhs(Rnodesr) += diag(Mr) .* gr(mesh.p(1,Rnodesr), mesh.p(2,Rnodesr))';
%! S(Rnodesl,Rnodesl) += Ml;
%! rhs(Rnodesl) += diag(Ml) .* gl(mesh.p(1,Rnodesl), mesh.p(2,Rnodesl))';
%! u = S\rhs; 
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-7)

%!test
%! n = 10;
%! [mesh] = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! uex    = @(r,z) exp(r);
%! duexdr = @(r,z) uex(r,z);
%! d2uexdr2 = @(r,z) uex(r,z);
%! duexdz = @(r,z) 0*uex(r,z);
%! d2uexdz2 = @(r,z) 0*uex(r,z);
%! Rnodesr  = bim2c_unknowns_on_side(mesh,[2]);
%! Rnodesl  = bim2c_unknowns_on_side(mesh,[4]);
%! Rnodesb  = bim2c_unknowns_on_side(mesh,[1]);
%! Rnodest  = bim2c_unknowns_on_side(mesh,[3]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! D = 1; vr = 1; vz = 0;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! beta   = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
%! gr = @(r,z) uex(r,z) - 1 * (-D*duexdr(r,z) + vr*uex(r,z));
%! gl = @(r,z) uex(r,z) - (-1) * (-D*duexdr(r,z) + vr*uex(r,z));
%! gb = @(r,z) uex(r,z) - (-1) * (-D*duexdz(r,z) + vz*uex(r,z));
%! gt = @(r,z) uex(r,z) - 1 * (-D*duexdz(r,z) + vz*uex(r,z));
%! rhs    = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! Mr = bim2a_axisymmetric_boundary_mass(mesh,2);  Ml = bim2a_axisymmetric_boundary_mass(mesh,4);
%! Mb = bim2a_axisymmetric_boundary_mass(mesh,1);  Mt = bim2a_axisymmetric_boundary_mass(mesh,3);
%! S(Rnodesr,Rnodesr) += Mr;
%! rhs(Rnodesr) += diag(Mr) .* gr(mesh.p(1,Rnodesr), mesh.p(2,Rnodesr))';
%! S(Rnodesl,Rnodesl) += Ml;
%! rhs(Rnodesl) += diag(Ml) .* gl(mesh.p(1,Rnodesl), mesh.p(2,Rnodesl))';
%! S(Rnodesb,Rnodesb) += Mb;
%! rhs(Rnodesb) += diag(Mb) .* gb(mesh.p(1,Rnodesb), mesh.p(2,Rnodesb))';
%! S(Rnodest,Rnodest) += Mt;
%! rhs(Rnodest) += diag(Mt) .* gt(mesh.p(1,Rnodest), mesh.p(2,Rnodest))';
%! u = S\rhs; 
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-7)
bim-1.1.8/inst/bim2a_axisymmetric_laplacian.m000066400000000000000000000053241502773057700212400ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{A}} = bim2a_axisymmetric_laplacian (@var{mesh},@var{epsilon},@var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration.
## Rotational symmetry is assumed with respect to be the vertical axis r=0. 
## Only plane geometries that DO NOT intersect the symmetry axis are admitted.
##
##@example
##@group
##    |   ____                 _|____ 
##    |  |    \               \ |    |
##  z |  |     \  OK           \|    |   NO!
##    |  |______\               |\___|
##    |     r                   |
#@end group 
#@end example
##
## The equation taken into account is:
##
## 1/r * d(r * Fr)/dr + dFz/dz = f
##
## with
##
## F = [Fr, Fz]' = - @var{epsilon} * @var{kappa} grad (u)
## 
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction, 
## bim2a_axisymmetric_advection_diffusion, bim2a_laplacian, bim1a_laplacian, 
## bim3a_laplacian}
## @end deftypefn

function [A] = bim2a_axisymmetric_laplacian(mesh,epsilon,kappa)

  ## Check input
  if nargin != 3
    error("bim2a_axisymmetric_laplacian: wrong number of input parameters.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_laplacian: the input mesh cannot intersect the rotation axis r=0.");
  endif

  ## Input check inside bim2a_axisymmetric_advection_diffusion
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);
  
  A = bim2a_axisymmetric_advection_diffusion (mesh,epsilon,kappa,ones(nnodes,1),0);

endfunction
bim-1.1.8/inst/bim2a_axisymmetric_reaction.m000066400000000000000000000122021502773057700211110ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{C}]} = @
## bim2a_axisymmetric_reaction(@var{mesh},@var{delta},@var{zeta}) 
##
## Build the lumped finite element mass matrix for a diffusion
## problem in cylindrical coordinates with axisymmetric configuration.
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
## 
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim2a_rhs, bim2a_axisymmetric_advection_diffusion, 
## bim2a_axisymmetric_laplacian, bim2a_reaction, bim1a_reaction, bim3a_reaction}
## @end deftypefn

function [C] = bim2a_axisymmetric_reaction(mesh,delta,zeta)

  ## Check input
  if nargin != 3
    error("bim2a_axisymmetric_reaction: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_axisymmetric_reaction: first input is not a valid mesh structure.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_reaction: the input mesh cannot intersect the rotation axis r=0.");
  endif
  
  nnodes = size(mesh.p,2);
  nelem  = size(mesh.t,2);

  r = abs (mesh.p(1,:));

  ## Turn scalar input to a vector of appropriate size
  if isscalar(delta)
    delta = delta*ones(nelem,1);
  endif
  if isscalar(zeta)
    zeta = zeta*ones(nnodes,1);
  endif

  if !( isvector(delta) && isvector(zeta) )
    error("bim2a_axisymmetric_reaction: coefficients are not valid vectors.");
  elseif length(delta) != nelem
    error("bim2a_axisymmetric_reaction: length of alpha is not equal to the number of elements.");
  elseif length(zeta) != nnodes
    error("bim2a_axisymmetric_reaction: length of gamma is not equal to the number of nodes.");
  endif

  wjacdet   = mesh.wjacdet(:,:);
  coeff     = zeta(mesh.t(1:3,:));
  coeffe    = delta(:);
  
  ## Local matrix	
  Blocmat = zeros(3,nelem);	
  for inode = 1:3
    Blocmat(inode,:) = coeffe'.*coeff(inode,:).*wjacdet(inode,:) .* r(mesh.t(inode,:));
  endfor
  
  gnode = (mesh.t(1:3,:));
  
  ## Global matrix
  C = sparse(gnode(:),gnode(:),Blocmat(:));

endfunction

%!shared mesh,delta,zeta,nnodes,nelem
% x = y = linspace(0,1,4);
% [mesh] = msh2m_structured_mesh(x,y,1,1:4);
% [mesh] = bim2c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% delta  = ones(columns(mesh.t),1);
% zeta   = ones(columns(mesh.p),1);
%!test
% [C] = bim2a_axisymmetric_reaction(mesh,delta,zeta);
% assert(size(C),[nnodes, nnodes]);
%!test
% [C1] = bim2a_axisymmetric_reaction(mesh,3*delta,zeta);
% [C2] = bim2a_axisymmetric_reaction(mesh,delta,3*zeta);
% assert(C1,C2);
%!test
% [C1] = bim2a_axisymmetric_reaction(mesh,3*delta,zeta);
% [C2] = bim2a_axisymmetric_reaction(mesh,3,1);
% assert(C1,C2);

%!test
%! n = 20;
%! [mesh] = msh2m_structured_mesh(linspace(1,2,n+1),linspace(0,1,n+1),1,1:4);
%! mesh   = bim2c_mesh_properties(mesh);
%! uex    = @(r,z) exp(r) .* exp(1-z);
%! duexdr = @(r,z) uex(r,z);
%! d2uexdr2 = @(r,z) uex(r,z);
%! duexdz = @(r,z) -uex(r,z);
%! d2uexdz2 = @(r,z) uex(r,z);
%! Dnodes = bim2c_unknowns_on_side(mesh,[1,2,3,4]);
%! Nnodes    = columns(mesh.p);
%! Nelements = columns(mesh.t);
%! Varnodes  = setdiff(1:Nnodes,Dnodes);
%! D = 1; vr = 1; vz = 1; sigma = 1;
%! alpha  = D*ones(Nelements,1);
%! gamma  = ones(Nnodes,1);
%! eta    = ones(Nnodes,1);
%! delta  = sigma*ones(columns(mesh.t),1);
%! zeta   = ones(columns(mesh.p),1);
%! beta   = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
%! f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
%!           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
%!           - D.*d2uexdz2(r,z) + vz * duexdz(r,z) ...
%!           + sigma * uex(r,z);
%! rhs    = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
%! S = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
%! C = bim2a_axisymmetric_reaction(mesh,delta,zeta);
%! S += C;
%! u = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
%! u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
%! assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-3)
bim-1.1.8/inst/bim2a_axisymmetric_rhs.m000066400000000000000000000071441502773057700201120ustar00rootroot00000000000000## Copyright (C) 2006-2014  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 
##  author: Matteo porro       
##  author: Emanuela Abbate    

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = @
## bim2a_axisymmetric_rhs(@var{mesh},@var{f},@var{g}) 
##
## Build the finite element right-hand side of a diffusion problem
## in cylindrical coordinates with axisymmetric configuration
## employing mass-lumping.
##
## The equation taken into account is:
##
## @var{delta} * u = f * g
## 
## where @var{f} is an element-wise constant scalar function, while
## @var{g} is a piecewise linear conforming scalar function.
## 
## @seealso{bim2a_axisymmetric_reaction, bim2a_axisymmetric_advection_diffusion, 
## bim2a_axisymmetric_laplacian, bim1a_axisymmetric_rhs}
## @end deftypefn

function b = bim2a_axisymmetric_rhs(mesh,f,g)

  ## Check input
  if (nargin != 3)
    error("bim2a_axisymmetric_rhs: wrong number of input parameters.");
  elseif !(isstruct(mesh) && isfield(mesh,"p") &&
	  isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_axisymmetric_rhs: first input is not a valid mesh structure.");
  elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
    error("bim2a_axisymmetric_rhs: the input mesh cannot intersect the rotation axis r=0.");
  endif
  
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);
  
  r = abs (mesh.p(1,:));

  ## Turn scalar input to a vector of appropriate size
  if isscalar(f)
    f = f*ones(nelem,1);
  endif
  if isscalar(g)
    g = g*ones(nnodes,1);
  endif

  if !( isvector(f) && isvector(g) )
    error("bim2a_axisymmetric_rhs: coefficients are not valid vectors.");
  elseif length(f) != nelem
    error("bim2a_axisymmetric_rhs: length of f is not equal to the number of elements.");
  elseif length(g) != nnodes
    error("bim2a_axisymmetric_rhs: length of g is not equal to the number of nodes.");
  endif

  g       = g(mesh.t(1:3,:));
  wjacdet = mesh.wjacdet;

  ## Build local matrix	
  Blocmat = zeros(3,nelem);	
  for inode = 1:3
    Blocmat(inode,:) = f'.*g(inode,:).*wjacdet(inode,:) .* r(mesh.t(inode,:));
  endfor

  gnode = (mesh.t(1:3,:));
  
  ## Assemble global matrix
  b = sparse(gnode(:),1,Blocmat(:));

endfunction

%!shared mesh,f,g,nnodes,nelem
% x = y = linspace(0,1,4);
% [mesh] = msh2m_structured_mesh(x,y,1,1:4);
% [mesh] = bim2c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% g      = ones(columns(mesh.t),1);
% f      = ones(columns(mesh.p),1);
%!test
% [b] = bim2a_axisymmetric_rhs(mesh,f,g);
% assert(size(b),[nnodes, 1]);
%!test
% [b1] = bim2a_axisymmetric_rhs(mesh,3*f,g);
% [b2] = bim2a_axisymmetric_rhs(mesh,f,3*g);
% assert(b1,b2);
%!test
% [b1] = bim2a_axisymmetric_rhs(mesh,3*f,g);
% [b2] = bim2a_axisymmetric_rhs(mesh,3,1);
% assert(b1,b2);
bim-1.1.8/inst/bim2a_boundary_mass.m000066400000000000000000000046131502773057700173640ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{M}]} = @
## bim2a_boundary_mass(@var{mesh},@var{sidelist},@var{nodelist})
##
## Build the lumped boundary mass matrix needed to apply Robin boundary
## conditions.   
##
## The vector @var{sidelist} contains the list of the side edges
## contributing to the mass matrix.
##
## The optional argument @var{nodelist} contains the list of the
## degrees of freedom on the boundary.
##
## @seealso{bim2a_rhs, bim2a_advection_diffusion, bim2a_laplacian,
## bim2a_reaction} 
## @end deftypefn

function [M] = bim2a_boundary_mass(mesh,sidelist,nodelist)

  ## Check input
  if nargin > 3
    error("bim2a_boundary_mass: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_boundary_mass: first input is not a valid mesh structure.");
  elseif !( isvector(sidelist) && isnumeric(sidelist) )
    error("bim2a_boundary_mass: second input is not a valid numeric vector.");
  endif

  if nargin<3
    [nodelist] = bim2c_unknowns_on_side(mesh,sidelist);
  endif

  edges = [];
  for ie = sidelist
    edges = [ edges,  mesh.e([1:2 5],mesh.e(5,:)==ie)];
  endfor
  l  = sqrt((mesh.p(1,edges(1,:))-mesh.p(1,edges(2,:))).^2 +
	    (mesh.p(2,edges(1,:))-mesh.p(2,edges(2,:))).^2);
  
  dd = zeros(size(nodelist));
  
  for in = 1:numel (nodelist)
    dd (in) = (sum(l(edges(1,:)==nodelist(in)))+sum(l(edges(2,:)==nodelist(in))))/2;
  endfor
  
  M = sparse(diag(dd));

endfunction
bim-1.1.8/inst/bim2a_laplacian.m000066400000000000000000000077401502773057700164460ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo,  Copyright (C) 2025 Carlo de Falco
## 
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{A}} = bim2a_laplacian (@var{mesh},@var{epsilon},@var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## - div (@var{epsilon} * @var{kappa} grad (u)) = f
## 
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim2a_rhs, bim2a_reaction, bim2a_advection_diffusion, bim1a_laplacian, bim3a_laplacian}
## @end deftypefn

function A = bim2a_laplacian (mesh, epsilon, kappa)

  ## Check input
  if nargin != 3
    error("bim2a_laplacian: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_laplacian: first input is not a valid mesh structure.");
  endif

  p      = mesh.p;
  t      = mesh.t;
  nnodes = columns(p);
  nelem  = columns(t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(epsilon)
    epsilon  = epsilon * ones (nelem, 1);
  endif
  if isscalar(kappa)
    kappa = kappa * ones (nnodes, 1);
  endif

  if !( isvector (epsilon) && isvector (kappa) && (numel (epsilon) == nelem) && (numel (kappa) == nnodes))
    error("bim2a_laplacian: coefficients are vectors of correct size.");
  endif

  ## Local element matrices (one 3x3 matrix for each triangle in the mesh)
  Lloc = zeros(3, 3, nelem);

  ## To integrate constants over each triangle we need to multiply by
  ## the triangle area. Multiply by the diffusion coefficient now tu
  ## simplify subsequent computations. Use inverse average for the
  ## diffusion coefficient.
  kappaepsilonareak = reshape (3./sum (1./kappa(:)(mesh.t (1:3)), 1)(:) .* epsilon(:) .* mesh.area(:), 1, 1, nelem);
  shg = mesh.shg(:,:,:);
  
  ## Computation
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum (shg(:,inode,:) .* shg(:,jnode,:), 1) .* kappaepsilonareak;
    endfor
  endfor

  ## Assemble the local (full) matrices into one global (sparse) matrix
  A = sparse (ginode(:), gjnode(:), Lloc(:));

endfunction

%!test
%! m = msh2m_structured_mesh (0:.1:5, 0:.1:1, 1, 1:4, 'random');
%! m = bim2c_mesh_properties (m);
%! A = bim2a_laplacian (m, 1, 3);
%! dnodes = bim2c_unknowns_on_side (m, 1:4);
%! inodes = setdiff (1:columns(m.p), dnodes);
%! u = m.p(1,:)';
%! u(inodes) = A(inodes, inodes) \ (-A(inodes, dnodes) * u(dnodes));
%! assert (u, m.p(1,:)', sqrt(eps))


%!demo
%! m = msh2m_structured_mesh (0:.1:2*pi, 0:.1:2*pi, 1, 1:4, 'random');
%! m = bim2c_mesh_properties (m);
%! kappa = 2 + sin (m.p(1, :)');
%! f     = kappa .* cos (m.p(2, :)');
%! uex   = cos (m.p(2, :)');
%! A = bim2a_laplacian (m, 3./(sum(1./kappa(m.t(1:3, :)), 1)), 1);
%! b = bim2a_rhs (m, 1, f);
%! dnodes = bim2c_unknowns_on_side (m, 1:4);
%! inodes = setdiff (1:columns(m.p), dnodes);
%! u = uex;
%! u(inodes) = A(inodes, inodes) \ (b(inodes)-A(inodes, dnodes) * u(dnodes));
%! h = pdesurf (m.p, m.t, u)
%! figure
%! pdesurf (m.p, m.t, uex)
bim-1.1.8/inst/bim2a_reaction.m000066400000000000000000000063311502773057700163210ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{C}]} = @
## bim2a_reaction(@var{mesh},@var{delta},@var{zeta}) 
##
## Build the lumped finite element mass matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
## 
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim2a_rhs, bim2a_advection_diffusion, bim2a_laplacian,
## bim1a_reaction, bim3a_reaction}
## @end deftypefn

function [C] = bim2a_reaction(mesh,delta,zeta)

  ## Check input
  if nargin != 3
    error("bim2a_reaction: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_reaction: first input is not a valid mesh structure.");
  endif

  nnodes = size(mesh.p,2);
  nelem  = size(mesh.t,2);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(delta)
    delta = delta*ones(nelem,1);
  endif
  if isscalar(zeta)
    zeta = zeta*ones(nnodes,1);
  endif

  if !( isvector(delta) && isvector(zeta) )
    error("bim2a_reaction: coefficients are not valid vectors.");
  elseif (numel (delta) != nelem)
    error("bim2a_: length of alpha is not equal to the number of elements.");
  elseif (numel (zeta) != nnodes)
    error("bim2a_: length of gamma is not equal to the number of nodes.");
  endif

  wjacdet   = mesh.wjacdet(:,:);
  coeff     = zeta(mesh.t(1:3,:));
  coeffe    = delta(:);
  
  ## Local matrix	
  Blocmat = zeros(3,nelem);	
  for inode = 1:3
    Blocmat(inode,:) = coeffe.'.*coeff(inode,:).*wjacdet(inode,:);
  endfor
  
  gnode = (mesh.t(1:3,:));
  
  ## Global matrix
  C = sparse(gnode(:),gnode(:),Blocmat(:));

endfunction

%!shared mesh,delta,zeta,nnodes,nelem
% x = y = linspace(0,1,4);
% [mesh] = msh2m_structured_mesh(x,y,,1:4;
% [mesh] = bim2c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% delta  = ones(columns(mesh.t),1);
% zeta   = ones(columns(mesh.p),1);
%!test
% [C] = bim2a_reaction(mesh,delta,zeta);
% assert(size(C),[nnodes, nnodes]);
%!test
% [C1] = bim2a_reaction(mesh,3*delta,zeta);
% [C2] = bim2a_reaction(mesh,delta,3*zeta);
% assert(C1,C2);
%!test
% [C1] = bim2a_reaction(mesh,3*delta,zeta);
% [C2] = bim2a_reaction(mesh,3,1);
% assert(C1,C2);
bim-1.1.8/inst/bim2a_rhs.m000066400000000000000000000060531502773057700153120ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = @
## bim2a_rhs(@var{mesh},@var{f},@var{g}) 
##
## Build the finite element right-hand side of a diffusion problem
## employing mass-lumping.
##
## The equation taken into account is:
##
## @var{delta} * u = f * g
## 
## where @var{f} is an element-wise constant scalar function, while
## @var{g} is a piecewise linear conforming scalar function.
## 
## @seealso{bim2a_reaction, bim2a_advection_diffusion, bim2a_laplacian,
## bim1a_reaction, bim3a_reaction}
## @end deftypefn

function b = bim2a_rhs(mesh,f,g)

  ## Check input
  if nargin != 3
    error("bim2a_rhs: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2a_rhs: first input is not a valid mesh structure.");
  endif

  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(f)
    f = f*ones(nelem,1);
  endif
  if isscalar(g)
    g = g*ones(nnodes,1);
  endif

  if !( isvector(f) && isvector(g) )
    error("bim2a_rhs: coefficients are not valid vectors.");
  elseif (numel (f) != nelem)
    error("bim2a_rhs: length of f is not equal to the number of elements.");
  elseif (numel (g) != nnodes)
    error("bim2a_rhs: length of g is not equal to the number of nodes.");
  endif

  g       = g(mesh.t(1:3,:));
  wjacdet = mesh.wjacdet;

  ## Build local matrix	
  Blocmat=zeros(3,nelem);	
  for inode=1:3
    Blocmat(inode,:) = f.' .* g(inode,:) .* wjacdet(inode,:);
  endfor

  gnode=(mesh.t(1:3,:));
  
  ## Assemble global matrix
  b = sparse(gnode(:),1,Blocmat(:));

endfunction

%!shared mesh,f,g,nnodes,nelem
% x = y = linspace(0,1,4);
% [mesh] = msh2m_structured_mesh(x,y,1,1:4);
% [mesh] = bim2c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% g      = ones(columns(mesh.t),1);
% f      = ones(columns(mesh.p),1);
%!test
% [b] = bim2a_rhs(mesh,f,g);
% assert(size(b),[nnodes, 1]);
%!test
% [b1] = bim2a_rhs(mesh,3*f,g);
% [b2] = bim2a_rhs(mesh,f,3*g);
% assert(b1,b2);
%!test
% [b1] = bim2a_rhs(mesh,3*f,g);
% [b2] = bim2a_rhs(mesh,3,1);
% assert(b1,b2);
bim-1.1.8/inst/bim2c_global_flux.m000066400000000000000000000134531502773057700170200ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{jx},@var{jy}]} = @
## bim2c_global_flux(@var{mesh},@var{u},@var{alpha},@var{gamma},@var{eta},@var{beta})
## 
## Compute the flux associated with the Scharfetter-Gummel approximation
## of the scalar field @var{u}.
##
## The vector field is defined as:
##
## J(@var{u}) = @var{alpha}* @var{gamma} * (@var{eta} * grad @var{u} - @var{beta} * @var{u}))
## 
## where @var{alpha} is an element-wise constant scalar function,
## @var{eta} and @var{gamma} are piecewise linear conforming scalar
## functions, while @var{beta} is element-wise constant vector function.
##
## J(@var{u}) is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function  @var{phi} as the last
## input.  In such case @var{beta} = grad @var{phi}  is assumed.  If
## @var{phi} is a single scalar value @var{beta}  is assumed to be 0 in
## the whole domain.
##
## @seealso{bim2c_pde_gradient,bim2a_advection_diffusion}
## @end deftypefn

function [jx, jy] = bim2c_global_flux(mesh,u,alpha,gamma,eta,beta)

  ## Check input
  if nargin != 6
    error("bim2c_global_flux: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2c_global_flux: first input is not a valid mesh structure.");
  endif
  
  nnodes = columns(mesh.p);
  nelem  = columns(mesh.t);
  

  if !( isvector(u) && isvector(alpha) && isvector(gamma) && isvector(eta) )
    error("bim2c_global_flux: coefficients are not valid vectors.");
  elseif (numel (u) != nnodes)
    error("bim2c_global_flux: length of u is not equal to the number of nodes.");
  elseif (numel (alpha) != nelem)
    error("bim2c_global_flux: length of alpha is not equal to the number of elements.");
  elseif (numel (gamma) != nnodes)
    error("bim2c_global_flux: length of gamma is not equal to the number of nodes.");
  elseif (numel (eta) != nnodes)
    error("bim2c_global_flux: length of eta is not equal to the number of nodes.");
  endif

  nelem  = columns(mesh.t);
  nnodes = columns(mesh.p);

  uloc      = u(mesh.t(1:3,:));

  shgx = reshape(mesh.shg(1,:,:),3,nelem);
  shgy = reshape(mesh.shg(2,:,:),3,nelem);

  x      = reshape(mesh.p(1,mesh.t(1:3,:)),3,[]);
  dx     = [ (x(3,:)-x(2,:)) ; 
	    (x(1,:)-x(3,:)) ;
	    (x(2,:)-x(1,:)) ];

  y      = reshape(mesh.p(2,mesh.t(1:3,:)),3,[]);
  dy     = [ (y(3,:)-y(2,:)) ; 
	    (y(1,:) -y(3,:)) ;
	    (y(2,:) -y(1,:)) ];

  if all(size(beta)==1)
    v12=0;v23=0;v31=0;
  elseif all(size(beta)==[2,nelem])
    v23    = beta(1,:) .* dx(1,:) + beta(2,:) .* dy(1,:);
    v31    = beta(1,:) .* dx(2,:) + beta(2,:) .* dy(2,:);
    v12    = beta(1,:) .* dx(3,:) + beta(2,:) .* dy(3,:);
  elseif all(size(beta)==[nnodes,1])
    betaloc = beta(mesh.t(1:3,:));
    v23    = betaloc(3,:)-betaloc(2,:);
    v31    = betaloc(1,:)-betaloc(3,:);
    v12    = betaloc(2,:)-betaloc(1,:);
  else
    error("bim2c_global_flux: coefficient beta has wrong dimensions.");
  endif
  
  etaloc = eta(mesh.t(1:3,:));
  
  eta23    = etaloc(3,:)-etaloc(2,:);
  eta31    = etaloc(1,:)-etaloc(3,:);
  eta12    = etaloc(2,:)-etaloc(1,:);
  
  etalocm1 = bimu_logm(etaloc(2,:),etaloc(3,:));
  etalocm2 = bimu_logm(etaloc(3,:),etaloc(1,:));
  etalocm3 = bimu_logm(etaloc(1,:),etaloc(2,:));
  
  gammaloc = gamma(mesh.t(1:3,:));
  geloc      = gammaloc.*etaloc;
  
  gelocm1 = bimu_logm(geloc(2,:),geloc(3,:));
  gelocm2 = bimu_logm(geloc(3,:),geloc(1,:));
  gelocm3 = bimu_logm(geloc(1,:),geloc(2,:));
  
  [bp23,bm23] = bimu_bernoulli( (v23 - eta23)./etalocm1);
  [bp31,bm31] = bimu_bernoulli( (v31 - eta31)./etalocm2);
  [bp12,bm12] = bimu_bernoulli( (v12 - eta12)./etalocm3);

  gfigfj = [ shgx(3,:) .* shgx(2,:) + shgy(3,:) .* shgy(2,:) ;
	    shgx(1,:) .* shgx(3,:) + shgy(1,:) .* shgy(3,:) ;
	    shgx(2,:) .* shgx(1,:) + shgy(2,:) .* shgy(1,:) ];

  jx = - alpha' .* ( gelocm1 .* etalocm1 .* dx(1,:) .*  ...         
		    gfigfj(1,:) .* ...
		    ( bp23 .* uloc(3,:)./etaloc(3,:) -...
		     bm23 .* uloc(2,:)./etaloc(2,:)) +... %% 1 
		    gelocm2 .* etalocm2 .* dx(2,:) .*  ...
		    gfigfj(2,:) .* ...
		    (bp31 .* uloc(1,:)./etaloc(1,:) -...
		     bm31 .* uloc(3,:)./etaloc(3,:)) +... %% 2
		    gelocm3 .* etalocm3 .* dx(3,:) .* ...
		    gfigfj(3,:) .* ...
		    (bp12 .* uloc(2,:)./etaloc(2,:) -...
		     bm12 .* uloc(1,:)./etaloc(1,:)) ... %% 3
		   );
		   
  jy = - alpha' .* ( gelocm1 .* etalocm1 .* dy(1,:) .*  ...         
		    gfigfj(1,:) .* ...
		    ( bp23 .* uloc(3,:)./etaloc(3,:) -...
		     bm23 .* uloc(2,:)./etaloc(2,:)) +... %% 1 
		    gelocm2 .* etalocm2 .* dy(2,:) .*  ...
		    gfigfj(2,:) .* ...
		    (bp31 .* uloc(1,:)./etaloc(1,:) -...
		     bm31 .* uloc(3,:)./etaloc(3,:)) +... %% 2
		    gelocm3 .* etalocm3 .* dy(3,:) .* ...
		    gfigfj(3,:) .* ...
		    (bp12 .* uloc(2,:)./etaloc(2,:) -...
		     bm12 .* uloc(1,:)./etaloc(1,:)) ... %% 3
		    );
endfunction
bim-1.1.8/inst/bim2c_intrp.m000066400000000000000000000041611502773057700156520ustar00rootroot00000000000000## Copyright (C) 2011, 2012 Carlo de Falco
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## .

## -*- texinfo -*-
##
## @deftypefn {Function File} {@var{data}} = bim2c_intrp (@var{msh}, @var{n_data}, @var{e_data}, @var{points}) 
##
## Compute interpolated values of multicomponent node centered field @var{n_data} and/or
## cell centered field @var{n_data} at an arbitrary set of points whose coordinates are given in the 
## n_by_2 matrix @var{points}. 
##
## @end deftypefn


## Author: Carlo de Falco 
## Created: 2012-10-01

function data = bim2c_intrp (msh, n_data, e_data, p)

  %% for each point, find the enclosing tetrahedron
  [t_list, b_list] = tsearchn (msh.p.', msh.t(1:3, :)', p);
    
  %% only keep points within tetrahedra
  invalid = isnan (t_list);
  t_list = t_list (! invalid);
  ntl = numel (t_list);
  b_list = b_list(! invalid, :);
  points(invalid,:) = [];

  data = [];
  if (! isempty (n_data))
    data = cat (1, data, squeeze (
                sum (reshape (n_data(msh.t(1:3, t_list), :),
                              [3, ntl, (columns (n_data))]) .* 
                     repmat (b_list.', [1, 1, (columns (n_data))]), 1)));
  endif

  if (! isempty (e_data))
    data = cat (1, data, e_data(t_list, :));
  endif

endfunction

%!test
%! msh = bim2c_mesh_properties (msh2m_structured_mesh (linspace (0, 1, 11), linspace (0, 1, 13), 1, 1:4));
%! x = y = linspace (0, 1, 100).';
%! u = msh.p(1, :).';
%! ui = bim2c_intrp (msh, u, [], [x, y]); 
%! assert (ui, linspace (0, 1, 100), 10*eps);
bim-1.1.8/inst/bim2c_mesh_properties.m000066400000000000000000000040701502773057700177250ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{omesh}]} = @
## bim2c_mesh_properties(@var{imesh}) 
##
## Compute the properties of @var{imesh} needed by BIM method and append
## them to @var{omesh} as fields.
##
## @seealso{bim2a_reaction, bim2a_advection_diffusion, bim2a_rhs,
## bim2a_laplacian, bim2a_boundary_mass}
## @end deftypefn

function [omesh] = bim2c_mesh_properties(imesh)

  ## Check input  
  if nargin != 1
    error("bim2c_mesh_properties: wrong number of input parameters.");
  elseif !(isstruct(imesh)     && isfield(imesh,"p") &&
	   isfield (imesh,"t") && isfield(imesh,"e"))
    error("bim2c_mesh_properties: first input is not a valid mesh structure.");
  endif

  omesh = imesh;
  [omesh.wjacdet,omesh.area,omesh.shg] = ...
      msh2m_geometrical_properties(imesh,"wjacdet","area","shg");

endfunction

%!shared mesh
% x = y = linspace(0,1,4);
% [mesh] = msh2m_structured_mesh(x,y,1,1:4);
% [mesh] = bim2c_mesh_properties(mesh);
%!test
% tmp = msh2m_geometrical_properties(mesh,"wjacdet");
% assert(mesh.wjacdet,tmp);
%!test
% tmp = msh2m_geometrical_properties(mesh,"shg");
% assert(mesh.shg,tmp);
%!test
% assert(mesh.area,sum(mesh.wjacdet,1));bim-1.1.8/inst/bim2c_norm.m000066400000000000000000000107741502773057700155000ustar00rootroot00000000000000## Copyright (C) 2006-2013  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Matteo Porro       

## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{norm_u}]} = @
## bim2c_norm(@var{mesh},@var{u},@var{norm_type}) 
##
## Compute the @var{norm_type}-norm of function @var{u} on the domain described
## by the triangular grid @var{mesh}.
##
## The input function @var{u} can be either a piecewise linear conforming scalar
## function or an elementwise constant scalar or vector function.
##
## The string parameter @var{norm_type} can be one among 'L2', 'H1' and 'inf'.
##
## Should the input function be piecewise constant, the H1 norm will not be 
## computed and the function will return an error message.
##
## For the numerical integration of the L2 norm the second order middle point
## quadrature rule is used.
##
## @seealso{bim1c_norm, bim3c_norm}
##
## @end deftypefn

function [norm_u] = bim2c_norm (m, u, norm_type)

  ## Check input  
  if (nargin != 3)
    error ("bim2c_norm: wrong number of input parameters.");
  elseif (! (isstruct (m) && isfield (m,"p")
          && isfield (m, "t") 
          && isfield (m, "e")))
    error ("bim2c_norm: first input is not a valid mesh structure.");
  endif

  nnodes = columns (m.p);
  nel    = columns (m.t);
  
  if (isequal (size (u), [2, nel]))
    u = u';
  endif
  
  if ((numel (u) != nnodes) && (rows (u) != nel))
    error ("bim2c_norm: numel(u) != nnodes and rows(u) != nel.");
  endif
  
  if (! (strcmp (norm_type,'L2') 
         || strcmp (norm_type,'inf') 
         || strcmp (norm_type,'H1'))) 
    error ("bim2c_norm: invalid norm type parameter.");
  endif

  if (strcmp (norm_type,'inf'))  
    norm_u = max (abs (u(:)));
  else
    if (numel (u) == nnodes)

      M = __mass_matrix__ (m);
      
      if (strcmp (norm_type, 'H1'))
        A = bim2a_laplacian (m, 1, 1);
        M += A;
      endif

      norm_u = sqrt(u' * M * u);
    
    else

      if (strcmp (norm_type, 'H1'))
        error (["bim2c_norm: cannot compute the H1 norm ", ... 
                "of an elementwise constant function."]);
      endif
      
      norm_u = m.area' * (norm (u, 2, 'rows').^2);      
      norm_u = sqrt (norm_u);

    endif
  endif

endfunction

function M = __mass_matrix__ (mesh)

  t      = mesh.t;
  nnodes = columns (mesh.p);
  nelem  = columns (t);

  ## Local contributions
  
  Mref = 1/12 * [2 1 1; 1 2 1; 1 1 2];
  area = reshape (mesh.area, 1, 1, nelem);
  
  ## Computation
  for inode = 1:3
    for jnode = 1:3
      ginode(inode,jnode,:) = t(inode,:);
      gjnode(inode,jnode,:) = t(jnode,:);
    endfor
  endfor
  Mloc = area .* Mref;

  ## assemble global matrix
  M = sparse (ginode(:), gjnode(:), Mloc(:), nnodes, nnodes);

endfunction

%!test
%!shared L, V, x, y, m
%! L = rand (1); V = rand (1); x = linspace (0,L,4);  y = x;
%! m = msh2m_structured_mesh (x,y,1,1:4);
%! m.area = msh2m_geometrical_properties (m, 'area');
%! m.shg  = msh2m_geometrical_properties (m, 'shg');
%! u    = V * ones (columns(m.p),1);
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2  = bim2c_norm (m, u, 'L2');
%! uH1  = bim2c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], [V, V*L, V*L], 1e-12);
%!test
%! u    = V * (m.p(1,:) + 2*m.p(2,:))';
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2  = bim2c_norm (m, u, 'L2');
%! uH1  = bim2c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], 
%!         [3*L*V, V*L^2*sqrt(8/3), V*sqrt(8/3*L^4 + 5*L^2)],
%!          1e-12);
%!test
%! u    = V * ones (columns(m.t),1);
%! uinf = bim2c_norm (m, u, 'inf');
%! uL2  = bim2c_norm (m, u, 'L2');
%! assert ([uinf, uL2], [V, V*L], 1e-12);
%!test
%! u     = V * ones (columns(m.t),1);
%! uvect = [u, 2*u];
%! uinf  = bim2c_norm (m, uvect, 'inf');
%! uL2   = bim2c_norm (m, uvect, 'L2');
%! assert ([uinf, uL2], [2*V, V*L*sqrt(5)], 1e-12);
bim-1.1.8/inst/bim2c_pde_gradient.m000066400000000000000000000034321502773057700171430ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{gx},@var{gy}]} = @
## bim2c_pde_gradient(@var{mesh},@var{u}) 
##
## Compute the gradient of the piecewise linear conforming scalar
## function @var{u}.
##
## @seealso{bim2c_global_flux}
## @end deftypefn

function [gx, gy] = bim2c_pde_gradient(mesh,u)

  ## Check input  
  if nargin != 2
    error("bim2c_pde_gradient: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2c_pde_gradient: first input is not a valid mesh structure.");
  endif

  nnodes = columns(mesh.p);

  if (numel (u) != nnodes)
    error("bim2c_pde_gradient: length(u) != nnodes.");
  endif

  shgx = reshape(mesh.shg(1,:,:),3,[]);
  gx   = sum(shgx.*u(mesh.t(1:3,:)),1);
  shgy = reshape(mesh.shg(2,:,:),3,[]);
  gy   = sum(shgy.*u(mesh.t(1:3,:)),1);

endfunction
bim-1.1.8/inst/bim2c_tri_to_nodes.m000066400000000000000000000052021502773057700172030ustar00rootroot00000000000000## Copyright (C) 2011 Carlo de Falco
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## .

## -*- texinfo -*-
##
## @deftypefn {Function File} {@var{u_nod}} = bim2c_tri_to_nodes (@var{mesh}, @var{u_tri}) 
## @deftypefnx {Function File} {@var{u_nod}} = bim2c_tri_to_nodes (@var{m_tri}, @var{u_tri}) 
## @deftypefnx {Function File} {[@var{u_nod}, @var{m_tri}]} = bim2c_tri_to_nodes ( ... ) 
##
## Compute interpolated values at triangle nodes @var{u_nod} given values at triangle mid-points @var{u_tri}.
## If called with more than one output, also return the interpolation matrix @var{m_tri} such that
## @code{u_nod = m_tri * u_tri}.
## If repeatedly performing interpolation on the same mesh the matrix @var{m_tri} obtained by a previous call 
## to @code{bim2c_tri_to_nodes} may be passed as input to avoid unnecessary computations.
##
## @end deftypefn


## Author: Carlo de Falco 
## Created: 2011-03-07

function [u_nod, m_tri] = bim2c_tri_to_nodes (m, u_tri)

  if (nargout > 1)
    if (isstruct (m))
      nel   = columns (m.t);
      nnod  = columns (m.p);
      ii    = m.t(1:3, :);
      jj    = repmat (1:nel, 3, 1);
      vv    = repmat (m.area(:)', 3, 1) / 3;
      m_tri = bim2a_reaction (m, 1, 1) \ sparse (ii, jj, vv, nnod, nel); 
    elseif (ismatrix (m))
      m_tri = m;
    else
      error ("bim2c_tri_to_nodes: first input parameter is of incorrect type");
    endif
    u_nod = m_tri * u_tri;
  else
    if (isstruct (m))
      rhs   = bim2a_rhs (m, u_tri, 1);
      mass  = bim2a_reaction (m, 1, 1);
      u_nod = full (mass \ rhs);
    elseif (ismatrix (m))
      u_nod = m * u_tri;
    else
      error ("bim2c_tri_to_nodes: first input parameter is of incorrect type");
    endif
  endif

endfunction

%!test
%! msh = bim2c_mesh_properties (msh2m_structured_mesh (linspace (0, 1, 3), linspace (0, 1, 3), 1, 1:4, "random"));
%! nel  = columns (msh.t);
%! nnod = columns (msh.p);
%! u_tri = randn (nel, 1);
%! un1 = bim2c_tri_to_nodes (msh, u_tri);
%! [un2, m] = bim2c_tri_to_nodes (msh, u_tri);
%! assert (un1, un2, 1e-10)
bim-1.1.8/inst/bim2c_unknowns_on_side.m000066400000000000000000000034031502773057700200760ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{nodelist}]} = @
## bim2c_unknowns_on_side(@var{mesh},@var{sidelist}) 
##
## Return the list of the mesh nodes that lie on the geometrical sides
## specified in @var{sidelist}.
##
## @seealso{bim3c_unknown_on_faces, bim2c_pde_gradient,
## bim2c_global_flux}
## @end deftypefn
  
function [nodelist] = bim2c_unknowns_on_side(mesh, sidelist)
	
  ## Check input  
  if nargin != 2
    error("bim2c_unknowns_on_side: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim2c_unknowns_on_side: first input is not a valid mesh structure.");
  elseif !isnumeric(sidelist)
    error("bim2c_unknowns_on_side: second input is not a valid numeric vector.");
  endif

  [nodelist] = msh2m_nodes_on_sides(mesh,sidelist);

endfunction
bim-1.1.8/inst/bim3a_advection_diffusion.m000066400000000000000000000072221502773057700205400ustar00rootroot00000000000000## Copyright (C) 2010  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim3a_advection_diffusion (@var{mesh}, @var{alpha}, @var{v})
##
## Build the Scharfetter-Gummel stabilized stiffness matrix for a
## diffusion-advection problem. 
## 
## The equation taken into account is:
##
## - div (@var{alpha} ( grad (u) - grad (@var{v}) u)) = f
##
## where @var{v} is a piecewise linear continuous scalar
## functions and @var{alpha} is a piecewise constant scalar function.
##
## @seealso{bim3a_rhs, bim3a_reaction, bim3a_laplacian, bim3c_mesh_properties}
## @end deftypefn


function SG = bim3a_advection_diffusion (mesh, acoeff, v)

  t = mesh.t;
  nnodes = columns (mesh.p);
  nelem = columns(t);

  ## Local contributions
  Lloc = zeros(4,4,nelem);

  epsilonareak = reshape (acoeff .* mesh.area', 1, 1, nelem);
  shg = mesh.shg(:,:,:);
  
  ## Computation
  for inode = 1:4
    for jnode = 1:4
      ginode(inode,jnode,:) = t(inode,:);
      gjnode(inode,jnode,:) = t(jnode,:);
      Lloc(inode,jnode,:)   = ...
	  sum( shg(:,inode,:) .* shg(:,jnode,:), 1) .* epsilonareak;
    endfor
  endfor	

  vloc = v(t(1:4, :));
  [bp12,bm12] = bimu_bernoulli (vloc(2,:)-vloc(1,:));
  [bp13,bm13] = bimu_bernoulli (vloc(3,:)-vloc(1,:));
  [bp14,bm14] = bimu_bernoulli (vloc(4,:)-vloc(1,:));
  [bp23,bm23] = bimu_bernoulli (vloc(3,:)-vloc(2,:));
  [bp24,bm24] = bimu_bernoulli (vloc(4,:)-vloc(2,:));
  [bp34,bm34] = bimu_bernoulli (vloc(4,:)-vloc(3,:));
  
  bp12 = reshape (bp12, 1, 1, nelem) .* Lloc(1,2,:);
  bm12 = reshape (bm12, 1, 1, nelem) .* Lloc(1,2,:);
  bp13 = reshape (bp13, 1, 1, nelem) .* Lloc(1,3,:);
  bm13 = reshape (bm13, 1, 1, nelem) .* Lloc(1,3,:);
  bp14 = reshape (bp14, 1, 1, nelem) .* Lloc(1,4,:);
  bm14 = reshape (bm14, 1, 1, nelem) .* Lloc(1,4,:);
  bp23 = reshape (bp23, 1, 1, nelem) .* Lloc(2,3,:);
  bm23 = reshape (bm23, 1, 1, nelem) .* Lloc(2,3,:);
  bp24 = reshape (bp24, 1, 1, nelem) .* Lloc(2,4,:);
  bm24 = reshape (bm24, 1, 1, nelem) .* Lloc(2,4,:);
  bp34 = reshape (bp34, 1, 1, nelem) .* Lloc(3,4,:);
  bm34 = reshape (bm34, 1, 1, nelem) .* Lloc(3,4,:);
  
  ## SGloc=[...
  ##        -bm12-bm13-bm14,bp12            ,bp13           ,bp14     
  ##        bm12           ,-bp12-bm23-bm24 ,bp23           ,bp24
  ##        bm13           ,bm23            ,-bp13-bp23-bm34,bp34
  ##        bm14           ,bm24            ,bm34           ,-bp14-bp24-bp34...
  ##        ];
  
  Sloc(1,1,:) = -bm12-bm13-bm14;
  Sloc(1,2,:) = bp12;
  Sloc(1,3,:) = bp13;
  Sloc(1,4,:) = bp14;

  Sloc(2,1,:) = bm12;
  Sloc(2,2,:) = -bp12-bm23-bm24; 
  Sloc(2,3,:) = bp23;
  Sloc(2,4,:) = bp24;

  Sloc(3,1,:) = bm13;
  Sloc(3,2,:) = bm23;
  Sloc(3,3,:) = -bp13-bp23-bm34;
  Sloc(3,4,:) = bp34;
  
  Sloc(4,1,:) = bm14;
  Sloc(4,2,:) = bm24;
  Sloc(4,3,:) = bm34;
  Sloc(4,4,:) = -bp14-bp24-bp34;

  ## assemble global matrix
  SG = sparse(ginode(:),gjnode(:),Sloc(:), nnodes, nnodes);

endfunction	

bim-1.1.8/inst/bim3a_boundary_mass.m000066400000000000000000000047751502773057700173760ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco 
##  author: Matteo Porro   

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{M}]} = @
## bim3a_boundary_mass(@var{mesh},@var{facelist},@var{nodelist})
##
## Build the lumped boundary mass matrix needed to apply Robin boundary
## conditions.
##
## The vector @var{facelist} contains the list of the faces contributing
## to the mass matrix.
##
## The optional argument @var{nodelist} contains the list of the
## degrees of freedom on the boundary.
##
## @seealso{bim3a_rhs, bim3a_advection_diffusion, bim3a_laplacian,
## bim3a_reaction, bim2a_boundary_mass} 
## @end deftypefn

function [M] = bim3a_boundary_mass (mesh, facelist, nodelist)

  ## Check input
  if (nargin > 3)
    error ("bim3a_boundary_mass: wrong number of input parameters.");
  elseif (! ((isstruct (mesh)) && (isfield (mesh, "p")) 
             && (isfield (mesh, "t")) && isfield(mesh, "e")))
    error (["bim3a_boundary_mass: first input", ...
            " is not a valid mesh structure."]);
  elseif (! ((isvector (facelist)) && (isnumeric (facelist))))
    error (["bim3a_boundary_mass: second ", ...
            "input is not a valid numeric vector."]);
  endif

  if (nargin < 3)
    [nodelist] = bim3c_unknowns_on_faces (mesh, facelist);
  endif

  p = mesh.p;
  t = [];
  for ie = facelist
    t = [t,  mesh.e([1:3 10], mesh.e(10,:) == ie)];
  endfor

  area = 1/2 * norm (cross (p(:,t(2,:))-p(:,t(1,:)), 
                            p(:,t(3,:))-p(:,t(1,:))), 
                     2, 'columns');
  
  dd = zeros (size (nodelist));
  
  for in = 1:numel (nodelist)
    dd (in) = 1/3 * sum (area (any (t(1:3,:) == nodelist(in))));
  endfor
  
  M = sparse (diag (dd));

endfunction

bim-1.1.8/inst/bim3a_laplacian.m000066400000000000000000000070051502773057700164410ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} @
## {@var{A}} = bim3a_laplacian (@var{mesh}, @var{epsilon}, @var{kappa})
##
## Build the standard finite element stiffness matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## - (@var{epsilon} * @var{kappa} ( u' ))' = f
## 
## where @var{epsilon} is an element-wise constant scalar function,
## while @var{kappa} is a piecewise linear conforming scalar function.
##
## @seealso{bim3a_rhs, bim3a_reaction, bim2a_laplacian, bim3a_laplacian}
## @end deftypefn

function [A] = bim3a_laplacian (mesh,epsilon,kappa)

  ## Check input
  if nargin != 3
    error("bim3a_laplacian: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim3a_laplacian: first input is not a valid mesh structure.");
  endif

  p      = mesh.p;
  t      = mesh.t;
  nnodes = columns(p);
  nelem  = columns(t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(epsilon)
    epsilon  = epsilon * ones(nelem,1);
  endif
  if isscalar(kappa)
    kappa = kappa*ones(nnodes,1);
  endif

  if !( isvector(epsilon) && isvector(kappa) )
    error("bim3a_laplacian: coefficients are not valid vectors.");
  elseif (numel (epsilon) != nelem)
    error("bim3a_laplacian: length of epsilon is not equal to the number of elements.");
  elseif (numel (kappa) != nnodes)
    error("bim2a_laplacian: length of kappa is not equal to the number of nodes.");
  endif

  ## Local contributions
  Lloc = zeros(4,4,nelem);

  kappaepsilonareak = reshape (4./sum (1./kappa(:)(mesh.t (1:4)), 1)(:) .* epsilon(:) .* mesh.area(:), 1, 1, nelem);
  shg = mesh.shg(:,:,:);
  
  ## Computation
  for inode = 1:4
    for jnode = 1:4
      ginode(inode,jnode,:) = mesh.t(inode,:);
      gjnode(inode,jnode,:) = mesh.t(jnode,:);
      Lloc(inode,jnode,:)   = sum( kappa(inode) * shg(:,inode,:) .* shg(:,jnode,:),1) .* kappaepsilonareak;
    endfor
  endfor

  ## Assembly
  A = sparse(ginode(:),gjnode(:),Lloc(:));

endfunction

%!shared mesh,epsilon,kappa,nnodes,nelem
% x = y = z = linspace(0,1,4);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6);
% [mesh] = bim3c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% epsilon = ones(columns(mesh.t),1);
% kappa   = ones(columns(mesh.p),1);
%!test
% [A] = bim3a_laplacian(mesh,epsilon,kappa);
% assert(size(A),[nnodes, nnodes]);
%!test
% [A1] = bim3a_laplacian(mesh,3*epsilon,kappa);
% [A2] = bim3a_laplacian(mesh,epsilon,3*kappa);
% assert(A1,A2);
%!test
% [A1] = bim3a_laplacian(mesh,epsilon,kappa);
% [A2] = bim3a_laplacian(mesh,1,1);
% assert(A1,A2);
bim-1.1.8/inst/bim3a_osc_advection_diffusion.m000066400000000000000000000266771502773057700214230ustar00rootroot00000000000000## Copyright (C) 2012  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = bim3a_osc_advection_diffusion (@var{mesh}, @var{alpha}, @var{v})
##
## Build the Scharfetter-Gummel stabilized OSC stiffness 
## matrix for a diffusion-advection problem. 
## 
## For details on the Orthogonal Subdomain Collocation (OSC) method
## see: M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998.
##
## The equation taken into account is:
##
## - div (@var{alpha} ( grad (u) - grad (@var{v}) u)) = f
##
## where @var{v} is a piecewise linear continuous scalar
## functions and @var{alpha} is a piecewise constant scalar function.
##
## @seealso{bim3a_rhs, bim3a_osc_laplacian, bim3a_reaction, bim3a_laplacian, bim3c_mesh_properties}
## @end deftypefn

function M = bim3a_osc_advection_diffusion (msh, epsilon, v)

  ## Check input
  if (nargin != 3)
    print_usage ();
  elseif (! (isstruct (msh)     
             && isfield (msh, "p") 
             && isfield (msh, "t") 
             && isfield (msh, "e")))
    error (["bim3a_laplacian: first input ", ...
            "is not a valid msh structure"]);
  endif

  nnodes = columns (msh.p);
  nelem  = columns (msh.t);

  ## Turn scalar input to a vector of appropriate size
  if (isscalar (epsilon))
    epsilon = epsilon * ones(nelem, 1);
  endif

  if (! isvector (epsilon))
    error ("bim3a_laplacian: coefficient is not a vector");
  elseif (numel (epsilon) != nelem)
    error (["bim3a_laplacian: length of epsilon is ", ...
            "not equal to the number of mesh elements"]);
  endif

  ## Avoid warnings for broadcasting
  warning ("off", "Octave:broadcast", "local")

  ## Local contributions
  Lloc = __osc_local_laplacian__ (msh.p, msh.t, msh.shg, epsilon, msh.area, nnodes, nelem);
  
  ## Stabilization
  if (isscalar (v))
    v = zeros (nelem, 1);
  endif

  vloc = v(msh.t(1:4, :));
  [bp12, bm12] = bimu_bernoulli (vloc(2,:)-vloc(1,:));
  [bp13, bm13] = bimu_bernoulli (vloc(3,:)-vloc(1,:));
  [bp14, bm14] = bimu_bernoulli (vloc(4,:)-vloc(1,:));
  [bp23, bm23] = bimu_bernoulli (vloc(3,:)-vloc(2,:));
  [bp24, bm24] = bimu_bernoulli (vloc(4,:)-vloc(2,:));
  [bp34, bm34] = bimu_bernoulli (vloc(4,:)-vloc(3,:));
  
  bp12 = reshape (bp12, 1, 1, nelem) .* Lloc(1,2,:);
  bm12 = reshape (bm12, 1, 1, nelem) .* Lloc(1,2,:);
  bp13 = reshape (bp13, 1, 1, nelem) .* Lloc(1,3,:);
  bm13 = reshape (bm13, 1, 1, nelem) .* Lloc(1,3,:);
  bp14 = reshape (bp14, 1, 1, nelem) .* Lloc(1,4,:);
  bm14 = reshape (bm14, 1, 1, nelem) .* Lloc(1,4,:);
  bp23 = reshape (bp23, 1, 1, nelem) .* Lloc(2,3,:);
  bm23 = reshape (bm23, 1, 1, nelem) .* Lloc(2,3,:);
  bp24 = reshape (bp24, 1, 1, nelem) .* Lloc(2,4,:);
  bm24 = reshape (bm24, 1, 1, nelem) .* Lloc(2,4,:);
  bp34 = reshape (bp34, 1, 1, nelem) .* Lloc(3,4,:);
  bm34 = reshape (bm34, 1, 1, nelem) .* Lloc(3,4,:);

  Sloc(1,1,:) = -bm12-bm13-bm14;
  Sloc(1,2,:) = bp12;
  Sloc(1,3,:) = bp13;
  Sloc(1,4,:) = bp14;

  Sloc(2,1,:) = bm12;
  Sloc(2,2,:) = -bp12-bm23-bm24; 
  Sloc(2,3,:) = bp23;
  Sloc(2,4,:) = bp24;

  Sloc(3,1,:) = bm13;
  Sloc(3,2,:) = bm23;
  Sloc(3,3,:) = -bp13-bp23-bm34;
  Sloc(3,4,:) = bp34;
  
  Sloc(4,1,:) = bm14;
  Sloc(4,2,:) = bm24;
  Sloc(4,3,:) = bm34;
  Sloc(4,4,:) = -bp14-bp24-bp34;

     
  ## Assembly
  for inode = 1:4
    for jnode = 1:4
      ginode(inode, jnode,:) = msh.t(inode, :);
      gjnode(inode, jnode,:) = msh.t(jnode, :);
    endfor
  endfor

  M = sparse (ginode(:), gjnode(:), Sloc(:), nnodes, nnodes);

endfunction

%!shared msh, epsilon, M, nnodes, nelem, x, y, z
%!test
%! msh = bim3c_mesh_properties (msh3m_structured_mesh (0:5, 0:5, 0:5, 1, 1:6));
%! x = msh.p (1, :).';
%! y = msh.p (2, :).';
%! z = msh.p (3, :).';
%! u = ones (size (x));
%! M = bim3a_osc_advection_diffusion (msh, 1, 0);
%! assert (M * u, zeros (size (u)), eps * 100)
%!test
%! u = x;
%! bnd = bim3c_unknowns_on_faces (msh, [1, 2]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = y;
%! bnd = bim3c_unknowns_on_faces (msh, [3, 4]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = z;
%! bnd = bim3c_unknowns_on_faces (msh, [5, 6]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = z;
%! bnd = bim3c_unknowns_on_faces (msh, [5, 6]);
%! int = setdiff (1:columns (msh.p), bnd);
%! M = bim3a_osc_advection_diffusion (msh, pi, 0);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! M = bim3a_osc_advection_diffusion (msh, 1, x);
%! assert (norm (sum (M, 1), inf), 0, eps * 100)
%!test
%! M = bim3a_osc_advection_diffusion (msh, 1, y);
%! assert (norm (sum (M, 1), inf), 0, eps * 100)
%!test
%! M = bim3a_osc_advection_diffusion (msh, 1, z);
%! assert (norm (sum (M, 1), inf), 0, eps * 100)

%!demo
%! gmsh_input = [["Point(1) = {0, 0, 0, .1};      \n"], ...
%! ["Point(2) = {1, 0, 0, .1};                    \n"], ...
%! ["Point(3) = {0, -.3, 0, .1};                  \n"], ...
%! ["Point(4) = {0, +.3, 0, .1};                  \n"], ...
%! ["Point(5) = {1, -.3, 0, .1};                  \n"], ...
%! ["Point(6) = {1, 0.3, 0, .1};                  \n"], ...
%! ["Point(7) = {0, 0, -.3, .1};                  \n"], ...
%! ["Point(8) = {0, 0, +.3, .1};                  \n"], ...
%! ["Point(9) = {1, 0, -.3, .1};                  \n"], ...
%! ["Point(10) = {1, 0, 0.3, .1};                 \n"], ...
%! ["Circle(1) = {4, 1, 7};                       \n"], ...
%! ["Circle(2) = {7, 1, 3};                       \n"], ...
%! ["Circle(3) = {3, 1, 8};                       \n"], ...
%! ["Circle(4) = {8, 1, 4};                       \n"], ...
%! ["Circle(5) = {6, 2, 9};                       \n"], ...
%! ["Circle(6) = {9, 2, 5};                       \n"], ...
%! ["Circle(7) = {5, 2, 10};                      \n"], ...
%! ["Circle(8) = {10, 2, 6};                      \n"], ...
%! ["Line(9) = {4, 6};                            \n"], ...
%! ["Line(10) = {3, 5};                           \n"], ...
%! ["Line(11) = {8, 10};                          \n"], ...
%! ["Line(12) = {7, 9};                           \n"], ...
%! ["Line Loop(13) = {4, 1, 2, 3};                \n"], ...
%! ["Plane Surface(14) = {13};                    \n"], ...
%! ["Line Loop(15) = {5, 6, 7, 8};                \n"], ...
%! ["Plane Surface(16) = {15};                    \n"], ...
%! ["Line Loop(17) = {9, -8, -11, 4};             \n"], ...
%! ["Ruled Surface(18) = {17};                    \n"], ...
%! ["Line Loop(19) = {12, -5, -9, 1};             \n"], ...
%! ["Ruled Surface(20) = {19};                    \n"], ...
%! ["Line Loop(21) = {12, 6, -10, -2};            \n"], ...
%! ["Ruled Surface(22) = {21};                    \n"], ...
%! ["Line Loop(23) = {11, -7, -10, 3};            \n"], ...
%! ["Ruled Surface(24) = {23};                    \n"], ...
%! ["Surface Loop(25) = {18, 20, 22, 16, 24, 14}; \n"], ...
%! ["Volume(26) = {25};                           \n"]];
%! fname = tmpnam ();
%! [fid, msg] = fopen (strcat (fname, ".geo"), "w");
%! if (fid < 0); error (msg); endif
%! fputs (fid, gmsh_input);
%! fclose (fid); 
%! msh = bim3c_mesh_properties (msh3m_gmsh (fname, "clscale", ".25"));
%! x = msh.p (1, :).';
%! u = x;
%! bnd = bim3c_unknowns_on_faces (msh, [14, 16]);
%! int = setdiff (1:columns (msh.p), bnd);
%! Mosc = bim3a_osc_advection_diffusion (msh, 1, msh.p(1,:)'*0);
%! Mgal = bim3a_advection_diffusion (msh, 1, msh.p(1,:)'*0);
%! u(int) = Mosc(int, int) \ ( - Mosc(int, bnd) * u(bnd));
%! uosc = u;
%! u(int) = Mgal(int, int) \ ( - Mgal(int, bnd) * u(bnd));
%! ugal = u;
%! fname_out = tmpnam ();
%! printf ("saving results to %s \n", strcat (fname_out, ".vtu"));
%! fpl_vtk_raw_write_field (fname_out, msh, {uosc, "u_osc"; ugal, "u_galerkin"}, {});
%! unlink (fname);

%!demo
%! gmsh_input = [["Point(1) = {0, 0, 0, .1};      \n"], ...
%! ["Point(2) = {1, 0, 0, .1};                    \n"], ...
%! ["Point(3) = {0, -.3, 0, .1};                  \n"], ...
%! ["Point(4) = {0, +.3, 0, .1};                  \n"], ...
%! ["Point(5) = {1, -.3, 0, .1};                  \n"], ...
%! ["Point(6) = {1, 0.3, 0, .1};                  \n"], ...
%! ["Point(7) = {0, 0, -.3, .1};                  \n"], ...
%! ["Point(8) = {0, 0, +.3, .1};                  \n"], ...
%! ["Point(9) = {1, 0, -.3, .1};                  \n"], ...
%! ["Point(10) = {1, 0, 0.3, .1};                 \n"], ...
%! ["Circle(1) = {4, 1, 7};                       \n"], ...
%! ["Circle(2) = {7, 1, 3};                       \n"], ...
%! ["Circle(3) = {3, 1, 8};                       \n"], ...
%! ["Circle(4) = {8, 1, 4};                       \n"], ...
%! ["Circle(5) = {6, 2, 9};                       \n"], ...
%! ["Circle(6) = {9, 2, 5};                       \n"], ...
%! ["Circle(7) = {5, 2, 10};                      \n"], ...
%! ["Circle(8) = {10, 2, 6};                      \n"], ...
%! ["Line(9) = {4, 6};                            \n"], ...
%! ["Line(10) = {3, 5};                           \n"], ...
%! ["Line(11) = {8, 10};                          \n"], ...
%! ["Line(12) = {7, 9};                           \n"], ...
%! ["Line Loop(13) = {4, 1, 2, 3};                \n"], ...
%! ["Plane Surface(14) = {13};                    \n"], ...
%! ["Line Loop(15) = {5, 6, 7, 8};                \n"], ...
%! ["Plane Surface(16) = {15};                    \n"], ...
%! ["Line Loop(17) = {9, -8, -11, 4};             \n"], ...
%! ["Ruled Surface(18) = {17};                    \n"], ...
%! ["Line Loop(19) = {12, -5, -9, 1};             \n"], ...
%! ["Ruled Surface(20) = {19};                    \n"], ...
%! ["Line Loop(21) = {12, 6, -10, -2};            \n"], ...
%! ["Ruled Surface(22) = {21};                    \n"], ...
%! ["Line Loop(23) = {11, -7, -10, 3};            \n"], ...
%! ["Ruled Surface(24) = {23};                    \n"], ...
%! ["Surface Loop(25) = {18, 20, 22, 16, 24, 14}; \n"], ...
%! ["Volume(26) = {25};                           \n"]];
%! fname = tmpnam (); 
%! [fid, msg] = fopen (strcat (fname, ".geo"), "w");
%! if (fid < 0); error (msg); endif
%! fputs (fid, gmsh_input);
%! fclose (fid); 
%! msh = bim3c_mesh_properties (msh3m_gmsh (fname, "clscale", ".25"));
%! x = msh.p (1, :).';
%! u = x;
%! bnd = bim3c_unknowns_on_faces (msh, [14, 16]);
%! int = setdiff (1:columns (msh.p), bnd);
%! Mosc = bim3a_osc_advection_diffusion (msh, 1, msh.p(1,:)'*0);
%! Mgal = bim3a_advection_diffusion (msh, 1, msh.p(1,:)'*0);
%! f = bim3a_rhs (msh, 10, 1);
%! u(int) = Mosc(int, int) \ (f(int) - Mosc(int, bnd) * u(bnd));
%! uosc = u;
%! u(int) = Mgal(int, int) \ (f(int) - Mgal(int, bnd) * u(bnd));
%! ugal = u;
%! fname_out = tmpnam ();
%! printf ("saving results to %s \n", strcat (fname_out, ".vtu"));
%! fpl_vtk_raw_write_field (fname_out, msh, {uosc, "u_osc"; ugal, "u_galerkin"}, {});
%! unlink (fname);
bim-1.1.8/inst/bim3a_osc_laplacian.m000066400000000000000000000073101502773057700173040ustar00rootroot00000000000000## Copyright (C) 2012  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     

## -*- texinfo -*-
## @deftypefn {Function File} @
## {@var{A}} = bim3a_osc_laplacian (@var{mesh}, @var{epsilon})
##
## Build the osc finite element stiffness matrix for a diffusion
## problem. 
##
## For details on the Orthogonal Subdomain Collocation (OSC) method
## see: M.Putti and C.Cordes, SIAM J.SCI.COMPUT. Vol.19(4), pp.1154-1168, 1998. 
##
## The equation taken into account is:
##
## - div (@var{epsilon} grad (u)) = f
## 
## where @var{epsilon} is an element-wise constant scalar function.
##
## @seealso{bim3a_rhs, bim3a_reaction, bim2a_laplacian, bim3a_laplacian}
## @end deftypefn

function M = bim3a_osc_laplacian (msh, epsilon)

  ## Check input
  if (nargin != 2)
    print_usage ();
  elseif (! (isstruct (msh)     
             && isfield (msh, "p") 
             && isfield (msh, "t") 
             && isfield (msh, "e")))
    error (["bim3a_osc_laplacian: first input ", ...
            "is not a valid msh structure"]);
  endif

  nnodes = columns (msh.p);
  nelem  = columns (msh.t);

  ## Turn scalar input to a vector of appropriate size
  if (isscalar (epsilon))
    epsilon = epsilon * ones (nelem, 1);
  endif

  if (! isvector (epsilon))
    error ("bim3a_osc_laplacian: coefficient is not a vector");
  elseif (numel (epsilon) != nelem)
    error (["bim3a_osc_laplacian: length of epsilon is ", ...
            "not equal to the number of mesh elements"]);
  endif

  ## Avoid warnings for broadcasting
  warning ("off", "Octave:broadcast", "local")

  ## Local contributions
  Lloc = __osc_local_laplacian__ (msh.p, msh.t, msh.shg, 
                                  epsilon, msh.area, nnodes, 
                                  nelem);

  ## Assembly
  for inode = 1:4
    for jnode = 1:4
      ginode(inode, jnode,:) = msh.t(inode, :);
      gjnode(inode, jnode,:) = msh.t(jnode, :);
    endfor
  endfor

  M = sparse (ginode(:), gjnode(:), Lloc(:), nnodes, nnodes);

endfunction

%!shared msh, epsilon, M, nnodes, nelem, x, y, z
%!test
%! msh = bim3c_mesh_properties (msh3m_structured_mesh (0:5, 0:5, 0:5, 1, 1:6));
%! x = msh.p (1, :).';
%! y = msh.p (2, :).';
%! z = msh.p (3, :).';
%! u = ones (size (x));
%! M = bim3a_osc_laplacian (msh, 1);
%! assert (M * u, zeros (size (u)), eps * 100)
%!test
%! u = x;
%! bnd = bim3c_unknowns_on_faces (msh, [1, 2]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = y;
%! bnd = bim3c_unknowns_on_faces (msh, [3, 4]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = z;
%! bnd = bim3c_unknowns_on_faces (msh, [5, 6]);
%! int = setdiff (1:columns (msh.p), bnd);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
%!test
%! u = z;
%! bnd = bim3c_unknowns_on_faces (msh, [5, 6]);
%! int = setdiff (1:columns (msh.p), bnd);
%! M = bim3a_osc_laplacian (msh, pi);
%! assert (M(int, int) * u(int), -M(int, bnd) * u(bnd), 100 * eps)
bim-1.1.8/inst/bim3a_reaction.m000066400000000000000000000062401502773057700163210ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} @
## {[@var{C}]} = bim3a_reaction (@var{mesh},@var{delta},@var{zeta})
##
## Build the lumped finite element mass matrix for a diffusion
## problem. 
##
## The equation taken into account is:
##
## @var{delta} * @var{zeta} * u = f
## 
## where @var{delta} is an element-wise constant scalar function, while
## @var{zeta} is a piecewise linear conforming scalar function.
##
## @seealso{bim3a_rhs, bim3a_laplacian, bim2a_reaction, bim3a_reaction}
## @end deftypefn

function [C] = bim3a_reaction (mesh,delta,zeta);

  ## Check input
  if nargin != 3
    error("bim3a_reaction: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim3a_reaction: first input is not a valid mesh structure.");
  endif

  nnodes    = columns (mesh.p);
  nelem     = columns (mesh.t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(delta)
    delta = delta*ones(nelem,1);
  endif
  if isscalar(zeta)
    zeta = zeta*ones(nnodes,1);
  endif

  if !( isvector(delta) && isvector(zeta) )
    error("bim3a_reaction: coefficients are not valid vectors.");
  elseif (numel (delta) != nelem)
    error("bim3a_: length of alpha is not equal to the number of elements.");
  elseif (numel (zeta) != nnodes)
    error("bim3a_: length of gamma is not equal to the number of nodes.");
  endif

  Cloc    = zeros(4,nelem);
  coeff   = zeta(mesh.t(1:4,:));
  coeffe  = delta;
  wjacdet = mesh.wjacdet;

  for inode = 1:4
    Cloc(inode,:) = coeffe'.*coeff(inode,:).*wjacdet(inode,:);
  endfor

  gnode = (mesh.t(1:4,:));

  ## Global matrix
  C = sparse(gnode(:),gnode(:),Cloc(:));

endfunction

%!shared mesh,delta,zeta,nnodes,nelem
% x = y = z = linspace(0,1,4);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6);
% [mesh] = bim3c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% delta  = ones(columns(mesh.t),1);
% zeta   = ones(columns(mesh.p),1);
%!test
% [C] = bim3a_reaction(mesh,delta,zeta);
% assert(size(C),[nnodes, nnodes]);
%!test
% [C1] = bim3a_reaction(mesh,3*delta,zeta);
% [C2] = bim3a_reaction(mesh,delta,3*zeta);
% assert(C1,C2);
%!test
% [C1] = bim2a_reaction(mesh,3*delta,zeta);
% [C2] = bim2a_reaction(mesh,3,1);
% assert(C1,C2);
bim-1.1.8/inst/bim3a_rhs.m000066400000000000000000000060401502773057700153070ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = @
## bim3a_rhs (@var{mesh}, @var{f}, @var{g}) 
##
## Build the finite element right-hand side of a diffusion problem
## employing mass-lumping.
##
## The equation taken into account is:
##
## @var{delta} * u =  @var{f} * @var{g}
## 
## where @var{f} is an element-wise constant scalar function, while
## @var{g} is a piecewise linear conforming scalar function.
## 
## @seealso{bim3a_reaction, bim3_laplacian, bim1a_reaction,
## bim2a_reaction} 
## @end deftypefn

function [b] = bim3a_rhs (mesh,f,g);

  ## Check input
  if nargin != 3
    error("bim3a_rhs: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim3a_rhs: first input is not a valid mesh structure.");
  endif

  nnodes    = columns (mesh.p);
  nelem     = columns (mesh.t);

  ## Turn scalar input to a vector of appropriate size
  if isscalar(f)
    f = f*ones(nelem,1);
  endif
  if isscalar(g)
    g = g*ones(nnodes,1);
  endif

  if !( isvector(f) && isvector(g) )
    error("bim3a_rhs: coefficients are not valid vectors.");
  elseif (numel (f) != nelem)
    error("bim3a_rhs: length of f is not equal to the number of elements.");
  elseif (numel (g) != nnodes)
    error("bim3a_rhs: length of g is not equal to the number of nodes.");
  endif

  bloc    = zeros(4,nelem);
  coeff   = g(mesh.t(1:4,:));
  coeffe  = f;
  wjacdet = mesh.wjacdet;

  for inode = 1:4
    bloc(inode,:) = coeffe'.*coeff(inode,:).*wjacdet(inode,:);
  endfor

  gnode = (mesh.t(1:4,:));

  ## Global matrix
  b = sparse(gnode(:),1,bloc(:));

endfunction

%!shared mesh,f,g,nnodes,nelem
% x = y = z = linspace(0,1,4);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6);
% [mesh] = bim3c_mesh_properties(mesh);
% nnodes = columns(mesh.p);
% nelem  = columns(mesh.t);
% g      = ones(columns(mesh.t),1);
% f      = ones(columns(mesh.p),1);
%!test
% [b] = bim3a_rhs(mesh,f,g);
% assert(size(b),[nnodes, 1]);
%!test
% [b1] = bim3a_rhs(mesh,3*f,g);
% [b2] = bim3a_rhs(mesh,f,3*g);
% assert(b1,b2);
%!test
% [b1] = bim2a_rhs(mesh,3*f,g);
% [b2] = bim2a_rhs(mesh,3,1);
% assert(b1,b2);
bim-1.1.8/inst/bim3c_global_flux.m000066400000000000000000000101371502773057700170150ustar00rootroot00000000000000## Copyright (C) 2012  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{F}]} = @
## bim3c_global_flux (@var{mesh}, @var{u}, @var{alpha}, @var{v})
##
## Compute the flux associated with the Scharfetter-Gummel approximation
## of the scalar field @var{u}.
##
## The vector field is defined as:
##
## F =- @var{alpha} ( grad (u) - grad (@var{v}) u ) 
##
## where @var{v} is a piecewise linear continuous scalar
## functions and @var{alpha} is a piecewise constant scalar function.
##
## @seealso{bim3a_rhs, bim3a_reaction, bim3a_laplacian, bim3c_mesh_properties}
## @end deftypefn


function F = bim3c_global_flux (mesh, u, acoeff, v)

  t     = mesh.t;
  nelem = columns (mesh.t);
  F     = zeros (3, nelem);

  ## Local contributions
  Lloc = zeros (4,4,nelem);

  epsilonareak = reshape (acoeff .* mesh.area', 1, 1, nelem);
  shg = mesh.shg(:,:,:);

  ## Computation
  for inode = 1:4
    for jnode = 1:4
      ginode(inode,jnode,:) = t(inode,:);
      gjnode(inode,jnode,:) = t(jnode,:);
      Lloc(inode,jnode,:)   = sum (shg(:,inode,:) .* shg(:,jnode,:), 1) ...
                              .* epsilonareak;
    endfor
  endfor

  uloc = u(t(1:4, :));
  vloc = v(t(1:4, :));
  [bp12,bm12] = bimu_bernoulli (vloc(2,:)-vloc(1,:));
  [bp13,bm13] = bimu_bernoulli (vloc(3,:)-vloc(1,:));
  [bp14,bm14] = bimu_bernoulli (vloc(4,:)-vloc(1,:));
  [bp23,bm23] = bimu_bernoulli (vloc(3,:)-vloc(2,:));
  [bp24,bm24] = bimu_bernoulli (vloc(4,:)-vloc(2,:));
  [bp34,bm34] = bimu_bernoulli (vloc(4,:)-vloc(3,:));
  
  bp12 = reshape (bp12, 1, 1, nelem) .* Lloc(1,2,:);
  bm12 = reshape (bm12, 1, 1, nelem) .* Lloc(1,2,:);
  bp13 = reshape (bp13, 1, 1, nelem) .* Lloc(1,3,:);
  bm13 = reshape (bm13, 1, 1, nelem) .* Lloc(1,3,:);
  bp14 = reshape (bp14, 1, 1, nelem) .* Lloc(1,4,:);
  bm14 = reshape (bm14, 1, 1, nelem) .* Lloc(1,4,:);
  bp23 = reshape (bp23, 1, 1, nelem) .* Lloc(2,3,:);
  bm23 = reshape (bm23, 1, 1, nelem) .* Lloc(2,3,:);
  bp24 = reshape (bp24, 1, 1, nelem) .* Lloc(2,4,:);
  bm24 = reshape (bm24, 1, 1, nelem) .* Lloc(2,4,:);
  bp34 = reshape (bp34, 1, 1, nelem) .* Lloc(3,4,:);
  bm34 = reshape (bm34, 1, 1, nelem) .* Lloc(3,4,:);
  
  ## SGloc=[...
  ##        -bm12-bm13-bm14,bp12            ,bp13           ,bp14     
  ##        bm12           ,-bp12-bm23-bm24 ,bp23           ,bp24
  ##        bm13           ,bm23            ,-bp13-bp23-bm34,bp34
  ##        bm14           ,bm24            ,bm34           ,-bp14-bp24-bp34
  ##        ];
  
  Sloc(1,1,:) = -bm12-bm13-bm14;
  Sloc(1,2,:) = bp12;
  Sloc(1,3,:) = bp13;
  Sloc(1,4,:) = bp14;

  Sloc(2,1,:) = bm12;
  Sloc(2,2,:) = -bp12-bm23-bm24; 
  Sloc(2,3,:) = bp23;
  Sloc(2,4,:) = bp24;

  Sloc(3,1,:) = bm13;
  Sloc(3,2,:) = bm23;
  Sloc(3,3,:) = -bp13-bp23-bm34;
  Sloc(3,4,:) = bp34;
  
  Sloc(4,1,:) = bm14;
  Sloc(4,2,:) = bm24;
  Sloc(4,3,:) = bm34;
  Sloc(4,4,:) = -bp14-bp24-bp34;

  r = zeros (4, nelem);
  f = zeros (3, nelem);
  
  for iel = 1:nelem

   r(:,iel) = Sloc(:,:,iel) * uloc(:,iel);
   f(:,iel) = Lloc(1:3, 1:3, iel) \ r(1:3, iel);

   F(:,iel) = shg(:,1:3, iel) * f(:, iel);

  endfor

endfunction

%!test
%! N = 10; pp = linspace (0, 1, N); msh = bim3c_mesh_properties (msh3m_structured_mesh (pp, pp, pp, 1, 1:6));
%! u = ones (N^3, 1);
%! v = ones (N^3, 1);
%! alpha = ones (columns (msh.t), 1);
%! F =  bim3c_global_flux (msh, u, alpha, v);
%! assert (norm (F(:), inf), 0, 100*eps);
bim-1.1.8/inst/bim3c_intrp.m000066400000000000000000000042271502773057700156560ustar00rootroot00000000000000## Copyright (C) 2011, 2012 Carlo de Falco
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## .

## -*- texinfo -*-
##
## @deftypefn {Function File} {@var{data}} = bim3c_intrp (@var{msh}, @var{n_data}, @var{e_data}, @var{points}) 
##
## Compute interpolated values of node centered multicomponent node centered field @var{n_data} and 
## cell centered field @var{n_data} at an arbitrary set of points whos coordinates are given in the 
## n_by_3 matrix  @var{points}. 
##
## @end deftypefn


## Author: Carlo de Falco 
## Created: 2012-10-01

function data = bim3c_intrp (msh, n_data, e_data, p)

  %% for each point, find the enclosing tetrahedron
  [t_list, b_list] = tsearchn (msh.p.', msh.t(1:4, :)', p);
    
  %% only keep points within tetrahedra
  invalid = isnan (t_list);
  t_list = t_list (! invalid);
  ntl = numel (t_list);
  b_list = b_list(! invalid, :);
  points(invalid,:) = [];

  data = [];
  if (! isempty (n_data))
    data = cat (1, data, squeeze (
                sum (reshape (n_data(msh.t(1:4, t_list), :),
                              [4, ntl, (columns (n_data))]) .* 
                     repmat (b_list.', [1, 1, (columns (n_data))]), 1)));
  endif

  if (! isempty (e_data))
    data = cat (1, data, e_data(t_list, :));
  endif

endfunction

%!test
%! msh = bim3c_mesh_properties (msh3m_structured_mesh (linspace (0, 1, 11), linspace (0, 1, 9), linspace (0, 1, 13), 1, 1:6));
%! x = y = z = linspace (0, 1, 100).';
%! u = msh.p(1, :).';
%! ui = bim3c_intrp (msh, u, [], [x, y, z]); 
%! assert (ui, linspace (0, 1, 100), 10*eps);bim-1.1.8/inst/bim3c_mesh_properties.m000066400000000000000000000041571502773057700177340ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{omesh}]} = @
## bim3c_mesh_properties(@var{imesh})
##
## Compute the properties of @var{imesh} needed by BIM method and append
## them to @var{omesh} as fields.
##
## @seealso{bim3a_reaction, bim3a_rhs, bim3a_laplacian}
## @end deftypefn

function [omesh] = bim3c_mesh_properties (imesh)

  ## Check input  
  if nargin != 1
    error("bim3c_mesh_properties: wrong number of input parameters.");
  elseif (! isstruct (imesh) || any (! isfield (imesh, {"p", "e", "t"}))) 
    error ("bim3c_mesh_properties: first input is not a valid mesh structure.");
  endif

  ## Compute properties
  omesh = imesh;
  [omesh.wjacdet,omesh.area,omesh.shg,omesh.shp] = ...
      msh3m_geometrical_properties (imesh, "wjacdet", "area", "shg", "shp");

endfunction

%!shared mesh
% x = y = z = linspace(0,1,4);
% mesh = msh3m_structured_mesh(x,y,z,1,1:6);
% mesh = bim3c_mesh_properties (mesh);
%!test
% tmp = msh3m_geometrical_properties (mesh, "wjacdet");
% assert(mesh.wjacdet,tmp);
%!test
% tmp = msh3m_geometrical_properties(mesh,"shg");
% assert(mesh.shg,tmp);
%!test
% tmp = msh3m_geometrical_properties(mesh,"shp");
% assert(mesh.shp,tmp);
%!test
% assert(mesh.area,sum(mesh.wjacdet,1));

bim-1.1.8/inst/bim3c_norm.m000066400000000000000000000115521502773057700154740ustar00rootroot00000000000000## Copyright (C) 2006-2013  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Matteo Porro       

## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{norm_u}]} = @
## bim3c_norm(@var{mesh},@var{u},@var{norm_type}) 
##
## Compute the @var{norm_type}-norm of function @var{u} on the domain described
## by the tetrahedral grid @var{mesh}.
##
## The input function @var{u} can be either a piecewise linear conforming scalar
## function or an elementwise constant scalar or vector function.
##
## The string parameter @var{norm_type} can be one among 'L2', 'H1' and 'inf'.
##
## Should the input function be piecewise constant, the H1 norm will not be 
## computed and the function will return an error message.
##
## For the numerical integration of the L2 norm the second order quadrature rule
## by Keast is used (ref. P. Keast, Moderate degree tetrahedral quadrature
## formulas, CMAME 55: 339-348 1986).
##
## @seealso{bim1c_norm, bim2c_norm}
##
## @end deftypefn

function [norm_u] = bim3c_norm (m, u, norm_type)

  ## Check input  
  if (nargin != 3)
    error ("bim3c_norm: wrong number of input parameters.");
  elseif (! (isstruct (m) && isfield (m,"p")) 
          && isfield (m, "t") && isfield (m, "e"))
    error ("bim3c_norm: first input is not a valid mesh structure.");
  endif

  nnodes = columns (m.p);
  nel    = columns (m.t);
  
  if (isequal (size (u), [3, nel]))
    u = u';
  endif
  
  if ((numel (u) != nnodes) && (rows (u) != nel))
    error ("bim3c_norm: length(u) != nnodes and rows(u) != nel.");
  endif
  
  if (! (strcmp (norm_type,'L2')
         || strcmp (norm_type,'inf') 
         || strcmp (norm_type,'H1')))
    error ("bim3c_norm: invalid norm type parameter.");
  endif

  if (strcmp (norm_type,'inf'))  
    norm_u = max (abs (u(:)));
  else
    if (numel (u) == nnodes)

      M = __mass_matrix__ (m);
      
      if (strcmp (norm_type, 'H1'))
        A = bim3a_laplacian (m, 1, 1);
        M += A;
      endif

      norm_u = sqrt(u' * M * u);
    
    else

      if (strcmp (norm_type, 'H1'))
        error (["bim3c_norm: cannot compute the H1 norm", ... 
                "of an elementwise constant function."]);
      endif
      
      norm_u = m.area * (norm (u', 2, 'cols').^2)';      
      norm_u = sqrt (norm_u);

    endif
  endif

endfunction

function M = __mass_matrix__ (mesh)

  t      = mesh.t;
  nnodes = columns (mesh.p);
  nelem  = columns (t);

  ## Local contributions
  a = (5 + 3 * sqrt (5)) / 20;   b = (5 - sqrt (5)) / 20;
  l1 = (1 - 3*b)^2 + 3*(1 - 2*b - a)^2;
  l2 = (1 - 3*b)*b + (1 - 2*b - a)*(a + 2*b);
  
  Mref = 1/4 * [l1 l2 l2 l2; 
                l2 l1 l2 l2; 
                l2 l2 l1 l2; 
                l2 l2 l2 l1];

  area = reshape (mesh.area, 1, 1, nelem);
  
  ## Computation
  for inode = 1:4
    for jnode = 1:4
      ginode(inode,jnode,:) = t(inode,:);
      gjnode(inode,jnode,:) = t(jnode,:);
    endfor
  endfor	
  Mloc = area .* Mref;

  ## assemble global matrix
  M = sparse (ginode(:), gjnode(:), Mloc(:), nnodes, nnodes);

endfunction

%!test
%!shared L, V, x, y, z, m
%! L = rand (1); V = rand (1); x = linspace (0,L,4);  y = x;  z = x;
%! m = msh3m_structured_mesh (x,y,z,1,1:6);
%! m.area = msh3m_geometrical_properties (m, 'area');
%! m.shg  = msh3m_geometrical_properties (m, 'shg');
%! u    = V * ones (columns(m.p),1);
%! uinf = bim3c_norm (m, u, 'inf');
%! uL2  = bim3c_norm (m, u, 'L2');
%! uH1  = bim3c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], [V, V*sqrt(L^3), V*sqrt(L^3)], 1e-12);
%!test
%! u    = V * (m.p(1,:) + 2*m.p(2,:) + 3*m.p(3,:))';
%! uinf = bim3c_norm (m, u, 'inf');
%! uL2  = bim3c_norm (m, u, 'L2');
%! uH1  = bim3c_norm (m, u, 'H1');
%! assert ([uinf, uL2, uH1], 
%!         [6*L*V, V*sqrt(61/6*L^5), V*sqrt(61/6*L^5 + 14*L^3)],
%!          1e-12);
%!test
%! u    = V * ones (columns(m.t),1);
%! uinf = bim3c_norm (m, u, 'inf');
%! uL2  = bim3c_norm (m, u, 'L2');
%! assert ([uinf, uL2], [V, V*sqrt(L^3)], 1e-12);
%!test
%! u     = V * ones (columns(m.t),1);
%! uvect = [u, 2*u, 3*u];
%! uinf  = bim3c_norm (m, uvect, 'inf');
%! uL2   = bim3c_norm (m, uvect, 'L2');
%! assert ([uinf, uL2], [3*V, V*sqrt(14*L^3)], 1e-12);
bim-1.1.8/inst/bim3c_pde_gradient.m000066400000000000000000000035261502773057700171500ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{gx}, @var{gy}, @var{gz}]} = @
## bim3c_pde_gradient(@var{mesh},@var{u}) 
##
## Compute the gradient of the piecewise linear conforming scalar
## function @var{u}.
##
## @seealso{bim3c_global_flux}
## @end deftypefn

function [gx, gy, gz] = bim3c_pde_gradient (mesh, u)

  ## Check input  
  if (nargin != 2)
    error("bim3c_pde_gradient: wrong number of input parameters.");
  elseif (! (isstruct (mesh) && isfield (mesh,"p")) &&
	   isfield (mesh, "t") && isfield(mesh, "e"))
    error ("bim3c_pde_gradient: first input is not a valid mesh structure.");
  endif

  nnodes = columns (mesh.p);

  if (numel (u) != nnodes)
    error ("bim3c_pde_gradient: length(u) != nnodes.");
  endif

  gx   = sum (squeeze (mesh.shg(1,:,:)) .* u(mesh.t(1:4,:)), 1);
  gy   = sum (squeeze (mesh.shg(2,:,:)) .* u(mesh.t(1:4,:)), 1);
  gz   = sum (squeeze (mesh.shg(3,:,:)) .* u(mesh.t(1:4,:)), 1);

endfunction
bim-1.1.8/inst/bim3c_tri_to_nodes.m000066400000000000000000000052261502773057700172120ustar00rootroot00000000000000## Copyright (C) 2011, 2012 Carlo de Falco
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING.  If not, see
## .

## -*- texinfo -*-
##
## @deftypefn {Function File} {@var{u_nod}} = bim3c_tri_to_nodes (@var{mesh}, @var{u_tri}) 
## @deftypefnx {Function File} {@var{u_nod}} = bim3c_tri_to_nodes (@var{m_tri}, @var{u_tri}) 
## @deftypefnx {Function File} {[@var{u_nod}, @var{m_tri}]} = bim3c_tri_to_nodes ( ... ) 
##
## Compute interpolated values at triangle nodes @var{u_nod} given values at tetrahedral centers of mass @var{u_tri}.
## If called with more than one output, also return the interpolation matrix @var{m_tri} such that
## @code{u_nod = m_tri * u_tri}.
## If repeatedly performing interpolation on the same mesh the matrix @var{m_tri} obtained by a previous call 
## to @code{bim2c_tri_to_nodes} may be passed as input to avoid unnecessary computations.
##
## @end deftypefn


## Author: Carlo de Falco 
## Created: 2011-03-07

function [u_nod, m_tri] = bim3c_tri_to_nodes (m, u_tri)

  if (nargout > 1)
    if (isstruct (m))
      nel  = columns (m.t);
      nnod = columns (m.p);
      ii = m.t(1:4, :);
      jj = repmat (1:nel, 4, 1);
      vv = repmat (m.area(:)', 4, 1) / 4;
      m_tri = bim3a_reaction (m, 1, 1) \ sparse (ii, jj, vv, nnod, nel);     
    elseif (ismatrix (m))
      m_tri = m;
    else
      error ("bim3c_tri_to_nodes: first input parameter is of incorrect type");
    endif
    u_nod = m_tri * u_tri;
  else
    if (isstruct (m))
      rhs   = bim3a_rhs (m, u_tri, 1);
      mass  = bim3a_reaction (m, 1, 1);
      u_nod = full (mass \ rhs);
    elseif (ismatrix (m))
      u_nod = m * u_tri;
    else
      error ("bim3c_tri_to_nodes: first input parameter is of incorrect type");
    endif
  endif

endfunction

%!test
%! msh = bim3c_mesh_properties (msh3m_structured_mesh (linspace (0, 1, 31), linspace (0, 1, 13), linspace (0, 1, 13), 1, 1:6));
%! nel  = columns (msh.t);
%! nnod = columns (msh.p);
%! u_tri = randn (nel, 1);
%! un1 = bim3c_tri_to_nodes (msh, u_tri);
%! [un2, m] = bim3c_tri_to_nodes (msh, u_tri);
%! assert (un1, un2, 1e-10)
bim-1.1.8/inst/bim3c_unknowns_on_faces.m000066400000000000000000000040351502773057700202360ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{nodelist}]} = @
## bim3c_unknowns_on_faces(@var{mesh},@var{facelist}) 
##
## Return the list of the mesh nodes that lie on the geometrical faces
## specified in @var{facelist}.
##
## @seealso{bim3c_unknown_on_faces, bim2c_pde_gradient,
## bim2c_global_flux}
##
## @end deftypefn
  
function [nodelist] = bim3c_unknowns_on_faces(mesh,facelist)

  ## Check input  
  if nargin != 2
    error("bim3c_unknowns_on_faces: wrong number of input parameters.");
  elseif !(isstruct(mesh)     && isfield(mesh,"p") &&
	   isfield (mesh,"t") && isfield(mesh,"e"))
    error("bim3c_unknowns_on_faces: first input is not a valid mesh structure.");
  elseif !isnumeric(facelist)
    error("bim3c_unknowns_on_faces: second input is not a valid numeric vector.");
  endif
	
  [nodelist] = msh3m_nodes_on_faces(mesh,facelist);

endfunction

%!shared mesh
% x = y = z = linspace(0,1,2);
% [mesh] = msh3m_structured_mesh(x,y,z,1,1:6);
%!test
% assert( bim3c_unknowns_on_faces(mesh, 1),[1 2 5 6] )
%!test
% assert( bim3c_unknowns_on_faces(mesh, 2),[3 4 7 8] )
%!test
% assert( bim3c_unknowns_on_faces(mesh, [1 2]),1:8)bim-1.1.8/inst/bimu_bernoulli.m000066400000000000000000000041371502773057700164540ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{bp}, @var{bn}]} = bimu_bernoulli (@var{x})
##
## Compute the values of the Bernoulli function corresponding to @var{x}
## and - @var{x} arguments. 
## 
## @seealso{bimu_logm}
## @end deftypefn

function [bp,bn] = bimu_bernoulli(x)

  ## Check input
  if nargin != 1
    error("bimu_bernoulli: wrong number of input parameters.");
  endif

  xlim= 1e-2;
  ax  = abs(x);
  bp  = zeros(size(x));
  bn  = bp;
  
  block1  = find(~ax);
  block21 = find((ax>80)&x>0);
  block22 = find((ax>80)&x<0);
  block3  = find((ax<=80)&(ax>xlim));
  block4  = find((ax<=xlim)&(ax~=0));
  
  ##  X=0
  bp(block1)=1.;
  bn(block1)=1.;
  
  ## ASYMPTOTICS
  bp(block21)=0.;
  bn(block21)=x(block21);
  bp(block22)=-x(block22);
  bn(block22)=0.;
  
  ## INTERMEDIATE VALUES
  bp(block3)=x(block3)./(exp(x(block3))-1);
  bn(block3)=x(block3)+bp(block3);
  
  ## SMALL VALUES
  if(any(block4))jj=1;
    fp=1.*ones(size(block4));
    fn=fp;
    df=fp;
    segno=1.;
    while (norm(df,inf) > eps),
      jj=jj+1;
      segno=-segno;
      df=df.*x(block4)/jj;
      fp=fp+df;
      fn=fn+segno*df;
    endwhile;
    bp(block4)=1./fp;
    bn(block4)=1./fn;
  endif
  
endfunction
bim-1.1.8/inst/bimu_logm.m000066400000000000000000000031211502773057700154070ustar00rootroot00000000000000## Copyright (C) 2006,2007,2008,2009,2010  Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     
##  author: Massimiliano Culpo 

## -*- texinfo -*-
## @deftypefn {Function File} @
## {[@var{T}]} = bimu_logm (@var{t1},@var{t2})
## 
## Input:
## @itemize @minus
## @item @var{t1}:
## @item @var{t2}:
## @end itemize
##
## Output:
## @itemize @minus
## @item @var{T}:
## @end itemize
##
## @seealso{bimu_bern}
## @end deftypefn

function [T] = bimu_logm(t1,t2)

  ## Check input
  if nargin != 2
    error("bimu_logm: wrong number of input parameters.");
  elseif size(t1) != size(t2)
    error("bimu_logm: t1 and t2 are of different size.");
  endif

  T = zeros(size(t2));
  
  sing     = abs(t2-t1)< 100*eps ;
  T(sing)  = (t2(sing)+t1(sing))/2;
  T(~sing) = (t2(~sing)-t1(~sing))./log(t2(~sing)./t1(~sing));

endfunction
bim-1.1.8/inst/private/000077500000000000000000000000001502773057700147345ustar00rootroot00000000000000bim-1.1.8/inst/private/__osc_local_laplacian__.m000066400000000000000000000100451502773057700216500ustar00rootroot00000000000000## Copyright (C) 2012  Carlo de Falco
##
## This file is part of:
##     BIM - Diffusion Advection Reaction PDE Solver
##
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see .
##
##  author: Carlo de Falco     

## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {@var{Lloc}} = __osc_local_laplacian__ @
## (@var{p}, @var{t}, @var{shg}, @var{epsilon}, @var{area}, @var{nnodes}, @var{nelem})
##
## Unocumented private function.
##
## @end deftypefn

function   Lloc = __osc_local_laplacian__ (p, t, shg, epsilon, area, nnodes, nelem)

  Lloc = zeros (4, 4, nelem);

  epsilonbyareak = epsilon(:) ./  abs (area(:)) / 48;
  A = zeros (3, 4, nelem);

  ## Computation
  for inode = 1:4
    A(:, inode, :) = 3 * abs (area) .* squeeze (shg (:, inode, :));
  endfor
  Ann = squeeze (sum (A .^ 2, 1));

  r12 = p(:, t (2, :)) - p(:, t (1, :));
  r13 = p(:, t (3, :)) - p(:, t (1, :));
  r14 = p(:, t (4, :)) - p(:, t (1, :));
  r23 = p(:, t (3, :)) - p(:, t (2, :));
  r24 = p(:, t (4, :)) - p(:, t (2, :));
  r34 = p(:, t (4, :)) - p(:, t (3, :));
  
  s12 = - epsilonbyareak .* (2 * (dot (r13,  r23,  1) .* 
                                  dot (r14,  r24,  1))(:) + 
                             squeeze (dot (A(:, 3, :), A(:, 4, :), 1)) .* 
                             (dot ( r13,  r23,  1) .^ 2 ./ Ann(4, :) + 
                              dot ( r14,  r24,  1).^ 2 ./ Ann(3, :))(:));

  s13 = - epsilonbyareak .* (2 * (dot (r12, -r23,  1) .* 
                                  dot (r14,  r34,  1))(:) + 
                             squeeze (dot (A(:, 2, :), A(:, 4, :), 1)) .* 
                             (dot ( r12, -r23, 1) .^ 2  ./ Ann(4, :) + 
                              dot ( r14,  r34,  1).^ 2 ./ Ann(2, :))(:));

  s14 = - epsilonbyareak .* (2 * (dot ( r12, -r24,  1) .* 
                                  dot ( r13, -r34,  1))(:) + 
                             squeeze (dot (A(:, 2, :), A(:, 3, :), 1)) .* 
                             (dot ( r12, -r24, 1) .^ 2  ./ Ann(3, :) + 
                              dot ( r13, -r34,  1).^ 2 ./ Ann(2, :))(:));

  s23 = - epsilonbyareak .* (2 * (dot (-r12, -r13,  1) .* 
                                  dot ( r24,  r34,  1))(:) + 
                             squeeze (dot (A(:, 1, :), A(:, 4, :), 1)) .* 
                             (dot (-r12, -r13, 1) .^ 2  ./ Ann(4, :) + 
                              dot ( r24,  r34,  1).^ 2 ./ Ann(1, :))(:));

  s24 = - epsilonbyareak .* (2 * (dot (-r12, -r14,  1) .* 
                                  dot ( r23, -r34,  1))(:) + 
                             squeeze (dot (A(:, 1, :), A(:, 3, :), 1)) .* 
                             (dot (-r12, -r14, 1) .^ 2  ./ Ann(3, :) + 
                              dot ( r23, -r34,  1).^ 2 ./ Ann(1, :))(:));

  s34 = - epsilonbyareak .* (2 * (dot (-r13, -r14,  1) .* 
                                  dot (-r23, -r24,  1))(:) + 
                             squeeze (dot (A(:, 1, :), A(:, 2, :), 1)) .*
                             (dot (-r13, -r14, 1) .^ 2  ./ Ann(2, :) + 
                              dot (-r23, -r24,  1).^ 2 ./ Ann(1, :))(:));
  
  Lloc(1, 2, :) = s12;  Lloc(2, 1, :) = s12;
  Lloc(1, 3, :) = s13;  Lloc(3, 1, :) = s13;
  Lloc(1, 4, :) = s14;  Lloc(4, 1, :) = s14;
  Lloc(1, 1, :) = -(s12+s13+s14);

  Lloc(2, 3, :) = s23;  Lloc(3, 2, :) = s23;
  Lloc(2, 4, :) = s24;  Lloc(4, 2, :) = s24;
  Lloc(2, 2, :) = -(s12+s23+s24);

  Lloc(3, 4, :) = s34;  Lloc(4, 3, :) = s34;
  Lloc(3, 3, :) = -(s13+s23+s34);

  Lloc(4, 4, :) = -(s14+s24+s34);

endfunction