X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fsecs2d-0.0.8%2FUtilities%2FUscharfettergummel3.m;fp=octave_packages%2Fsecs2d-0.0.8%2FUtilities%2FUscharfettergummel3.m;h=252cc4edbc42bb1018bb34bfd0eaf261fa47c63c;hp=0000000000000000000000000000000000000000;hb=f5f7a74bd8a4900f0b797da6783be80e11a68d86;hpb=1705066eceaaea976f010f669ce8e972f3734b05 diff --git a/octave_packages/secs2d-0.0.8/Utilities/Uscharfettergummel3.m b/octave_packages/secs2d-0.0.8/Utilities/Uscharfettergummel3.m new file mode 100644 index 0000000..252cc4e --- /dev/null +++ b/octave_packages/secs2d-0.0.8/Utilities/Uscharfettergummel3.m @@ -0,0 +1,290 @@ +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 . + + + 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) +