/usr/share/octave/packages/bim-1.1.5/bim3c_global_flux.m is in octave-bim 1.1.5-4.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 | ## 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 <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## -*- 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);
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