/usr/share/octave/packages/bim-1.1.5/bim2c_global_flux.m is in octave-bim 1.1.5-4.
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##
## 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>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## -*- 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
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