--- /dev/null
+function S = Uscharfettergummel3(mesh,alpha,gamma,eta,beta)
+
+ ## -*- texinfo -*-
+ ##
+ ## @deftypefn {Function File} @
+ ## {@var{S}} = Uscharfettergummel3 (@var{mesh}, @var{alpha}, @
+ ## @var{gamma}, @var{eta}, @var{beta})
+ ##
+ ##
+ ## Builds the Scharfetter-Gummel matrix for the
+ ## discretization of the LHS
+ ## of the equation:
+ ##
+ ## @iftex
+ ## @tex
+ ## $ -div ( \alpha \gamma ( \eta \vect{\nabla} u - \vect{beta} u )) = f $
+ ## @end tex
+ ## @end iftex
+ ## @ifinfo
+ ## -div (@var{alpha} * @var{gamma} (@var{eta} grad u - @var{beta} u )) = f
+ ## @end ifinfo
+ ##
+ ## where:
+ ## @itemize @minus
+ ## @item @var{alpha} is an element-wise constant scalar function
+ ## @item @var{eta}, @var{gamma} are piecewise linear conforming
+ ## scalar functions
+ ## @item @var{beta} is an element-wise constant vector function
+ ## @end itemize
+ ##
+ ## 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.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
+ ## mesh = Umeshproperties(mesh);
+ ## x = mesh.p(1,:)';
+ ## Dnodes = Unodesonside(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 = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
+ ## S = Uscharfettergummel3(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)
+ ## @end example
+ ##
+ ## @seealso{Ucomplap, Ucompconst, Ucompmass2, Uscharfettergummel}
+ ## @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.
+ %%
+ %% You should have received a copy of the GNU General Public License
+ %% along with SECS2D; If not, see <http://www.gnu.org/licenses/>.
+
+
+ Nnodes = columns(mesh.p);
+ Nelements = columns(mesh.t);
+
+ alphaareak = reshape (alpha.*sum( mesh.wjacdet,1)',1,1,Nelements);
+ shg = mesh.shg(:,:,:);
+
+
+ % build local Laplacian matrix
+
+ Lloc=zeros(3,3,Nelements);
+
+ 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;
+ end
+ end
+
+
+ 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,Nelements])
+ 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,:);
+ end
+
+ etaloc = eta(mesh.t(1:3,:));
+
+ eta12 = etaloc(2,:)-etaloc(1,:);
+ eta23 = etaloc(3,:)-etaloc(2,:);
+ eta31 = etaloc(1,:)-etaloc(3,:);
+
+ 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,:));
+
+ [bp12,bm12] = Ubern( (v12 - eta12)./etalocm3);
+ [bp23,bm23] = Ubern( (v23 - eta23)./etalocm1);
+ [bp31,bm31] = Ubern( (v31 - eta31)./etalocm2);
+
+ bp12 = reshape(gelocm3.*etalocm3.*bp12,1,1,Nelements).*Lloc(1,2,:);
+ bm12 = reshape(gelocm3.*etalocm3.*bm12,1,1,Nelements).*Lloc(1,2,:);
+ bp23 = reshape(gelocm1.*etalocm1.*bp23,1,1,Nelements).*Lloc(2,3,:);
+ bm23 = reshape(gelocm1.*etalocm1.*bm23,1,1,Nelements).*Lloc(2,3,:);
+ bp31 = reshape(gelocm2.*etalocm2.*bp31,1,1,Nelements).*Lloc(3,1,:);
+ bm31 = reshape(gelocm2.*etalocm2.*bm31,1,1,Nelements).*Lloc(3,1,:);
+
+ Sloc(1,1,:) = (-bm12-bp31)./reshape(etaloc(1,:),1,1,Nelements);
+ Sloc(1,2,:) = bp12./reshape(etaloc(2,:),1,1,Nelements);
+ Sloc(1,3,:) = bm31./reshape(etaloc(3,:),1,1,Nelements);
+
+ Sloc(2,1,:) = bm12./reshape(etaloc(1,:),1,1,Nelements);
+ Sloc(2,2,:) = (-bp12-bm23)./reshape(etaloc(2,:),1,1,Nelements);
+ Sloc(2,3,:) = bp23./reshape(etaloc(3,:),1,1,Nelements);
+
+ Sloc(3,1,:) = bp31./reshape(etaloc(1,:),1,1,Nelements);
+ Sloc(3,2,:) = bm23./reshape(etaloc(2,:),1,1,Nelements);
+ Sloc(3,3,:) = (-bm31-bp23)./reshape(etaloc(3,:),1,1,Nelements);
+
+ S = sparse(ginode(:),gjnode(:),Sloc(:));
+
+endfunction
+
+%!test
+%! [mesh.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:1/3:1],[0:1/3:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ones(Nnodes,1),ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:1/1e3:1],[0:1/2:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ff,ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:1/1e3:1],[0:1/2:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ff,ones(Nelements,1));
+%! S = Uscharfettergummel3(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.p,mesh.e,mesh.t] = Ustructmesh([0:.1:1],[0:.1:1],1,1:4);
+%! mesh = Umeshproperties(mesh);
+%! x = mesh.p(1,:)';y = mesh.p(2,:)';
+%! Dnodes = Unodesonside(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 = Ucompconst(mesh,ff,ones(Nelements,1));
+%! S = Uscharfettergummel3(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)
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff