/usr/share/octave/packages/secs2d-0.0.8/Utilities/Ufvsgcurrent3.m is in octave-secs2d 0.0.8-5.
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## -*- texinfo -*-
##
## @deftypefn {Function File} {[@var{jx},@var{jy}]} = Ufvsgcurrent3 @
## (@var{mesh}, @var{u}, @var{alpha}, @var{gamma}, @var{eta}, @var{beta});
##
##
## Builds the Scharfetter-Gummel approximation of the vector
## field
##
## @iftex
## @tex
## $ \vect{J}(u) = \alpha \gamma (\eta\vect{\nabla}u-\vect{beta}u) $
## @end tex
## @end iftex
## @ifinfo
## J(@var{u}) = @var{alpha}* @var{gamma} * (@var{eta} * grad @var{u} - @var{beta} * @var{u}))
## @end ifinfo
##
## where:
## @itemize @minus
## @item @var{alpha} is an element-wise constant scalar function
## @item @var{eta}, @var{u}, @var{gamma} are piecewise linear
## conforming scalar functions
## @item @var{beta} is an element-wise constant vector function
## @end itemize
##
## 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{Uscharfettergummel3}
## @end deftypefn
%% This file is part of
%%
%% SECS2D - A 2-D Drift--Diffusion Semiconductor Device Simulator
%% -------------------------------------------------------------------
%% Copyright (C) 2004-2006 Carlo de Falco
%%
%%
%%
%% SECS2D 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.
%%
%% SECS2D 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.
%%
%% Youx should have received a copy of the GNU General Public License
%% along with SECS2D; If not, see <http://www.gnu.org/licenses/>.
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,:)) ];
##ei = sqrt( dx.^2 + dy.^2 );
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,:);
end
etaloc = eta(mesh.t(1:3,:));
eta23 = etaloc(3,:)-etaloc(2,:);
eta31 = etaloc(1,:)-etaloc(3,:);
eta12 = etaloc(2,:)-etaloc(1,:);
etalocm1 = Utemplogm(etaloc(2,:),etaloc(3,:));
etalocm2 = Utemplogm(etaloc(3,:),etaloc(1,:));
etalocm3 = Utemplogm(etaloc(1,:),etaloc(2,:));
gammaloc = gamma(mesh.t(1:3,:));
geloc = gammaloc.*etaloc;
gelocm1 = Utemplogm(geloc(2,:),geloc(3,:));
gelocm2 = Utemplogm(geloc(3,:),geloc(1,:));
gelocm3 = Utemplogm(geloc(1,:),geloc(2,:));
[bp23,bm23] = Ubern( (v23 - eta23)./etalocm1);
[bp31,bm31] = Ubern( (v31 - eta31)./etalocm2);
[bp12,bm12] = Ubern( (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,:) ];
Fx = - 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
);
Fy = - 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
);
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