--- /dev/null
+function [V,n,p,res,niter] = DDGOXnlpoisson (mesh,Dsides,Sinodes,SiDnodes,...
+ Sielements,Vin,nin,pin,...
+ Fnin,Fpin,D,l2,l2ox,...
+ toll,maxit,verbose)
+
+%
+% [V,n,p,res,niter] = DDGOXnlpoisson (mesh,Dsides,Sinodes,Vin,nin,pin,...
+% Fnin,Fpin,D,l2,l2ox,toll,maxit,verbose)
+%
+% solves $$ -\lambda^2 V'' + (n(V,Fn) - p(V,Fp) -D)$$
+%
+
+
+% 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/>.
+
+global DDGOXNLPOISSON_LAP DDGOXNLPOISSON_MASS DDGOXNLPOISSON_RHS
+
+%% Set some useful constants
+dampit = 10;
+dampcoeff = 2;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% convert input vectors to columns
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+if Ucolumns(D)>Urows(D)
+ D=D';
+end
+
+
+if Ucolumns(nin)>Urows(nin)
+ nin=nin';
+end
+
+if Ucolumns(pin)>Urows(pin)
+ pin=pin';
+end
+
+if Ucolumns(Vin)>Urows(Vin)
+ Vin=Vin';
+end
+
+if Ucolumns(Fnin)>Urows(Fnin)
+ Fnin=Fnin';
+end
+
+if Ucolumns(Fpin)>Urows(Fpin)
+ Fpin=Fpin';
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% setup FEM data structures
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+nodes=mesh.p;
+elements=mesh.t;
+Nnodes = length(nodes);
+Nelements = length(elements);
+
+% Set list of nodes with Dirichelet BCs
+Dnodes = Unodesonside(mesh,Dsides);
+
+% Set values of Dirichelet BCs
+Bc = zeros(length(Dnodes),1);
+% Set list of nodes without Dirichelet BCs
+Varnodes = setdiff([1:Nnodes],Dnodes);
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%
+%% initialization:
+%% we're going to solve
+%% $$ - \lambda^2 (\delta V)'' + (\frac{\partial n}{\partial V} - \frac{\partial p}{\partial V})= -R $$
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%% set $$ n_1 = nin $$ and $$ V = Vin $$
+V = Vin;
+Fn = Fnin;
+Fp = Fpin;
+n = exp(V(Sinodes)-Fn);
+p = exp(-V(Sinodes)+Fp);
+n(SiDnodes) = nin(SiDnodes);
+p(SiDnodes) = pin(SiDnodes);
+
+
+%%%
+%%% Compute LHS matrices
+%%%
+
+%% let's compute FEM approximation of $$ L = - \frac{d^2}{x^2} $$
+if (isempty(DDGOXNLPOISSON_LAP))
+ coeff = l2ox * ones(Nelements,1);
+ coeff(Sielements)=l2;
+ DDGOXNLPOISSON_LAP = Ucomplap (mesh,coeff);
+end
+
+%% compute $$ Mv = ( n + p) $$
+%% and the (lumped) mass matrix M
+if (isempty(DDGOXNLPOISSON_MASS))
+ coeffe = zeros(Nelements,1);
+ coeffe(Sielements)=1;
+ DDGOXNLPOISSON_MASS = Ucompmass2(mesh,ones(Nnodes,1),coeffe);
+end
+freecarr=zeros(Nnodes,1);
+freecarr(Sinodes)=(n + p);
+Mv = freecarr;
+M = DDGOXNLPOISSON_MASS*spdiag(Mv);
+
+%%%
+%%% Compute RHS vector (-residual)
+%%%
+
+%% now compute $$ T0 = \frac{q}{\epsilon} (n - p - D) $$
+if (isempty(DDGOXNLPOISSON_RHS))
+ coeffe = zeros(Nelements,1);
+ coeffe(Sielements)=1;
+ DDGOXNLPOISSON_RHS = Ucompconst (mesh,ones(Nnodes,1),coeffe);
+end
+totcharge = zeros(Nnodes,1);
+totcharge(Sinodes)=(n - p - D);
+Tv0 = totcharge;
+T0 = Tv0 .* DDGOXNLPOISSON_RHS;
+
+%% now we're ready to build LHS matrix and RHS of the linear system for 1st Newton step
+A = DDGOXNLPOISSON_LAP + M;
+R = DDGOXNLPOISSON_LAP * V + T0;
+
+%% Apply boundary conditions
+A (Dnodes,:) = [];
+A (:,Dnodes) = [];
+R(Dnodes) = [];
+
+%% we need $$ \norm{R_1} $$ and $$ \norm{R_k} $$ for the convergence test
+normr(1) = norm(R,inf);
+relresnorm = 1;
+reldVnorm = 1;
+normrnew = normr(1);
+dV = V*0;
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%
+%% START OF THE NEWTON CYCLE
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+for newtit=1:maxit
+ if (verbose>0)
+ fprintf(1,'\n***\nNewton iteration: %d, reldVnorm = %e\n***\n',newtit,reldVnorm);
+ end
+
+% A(1,end)=realmin;
+ dV(Varnodes) =(A)\(-R);
+ dV(Dnodes)=0;
+
+
+ %%%%%%%%%%%%%%%%%%
+ %% Start of th damping procedure
+ %%%%%%%%%%%%%%%%%%
+ tk = 1;
+ for dit = 1:dampit
+ if (verbose>0)
+ fprintf(1,'\ndamping iteration: %d, residual norm = %e\n',dit,normrnew);
+ end
+ Vnew = V + tk * dV;
+
+ n = exp(Vnew(Sinodes)-Fn);
+ p = exp(-Vnew(Sinodes)+Fp);
+ n(SiDnodes) = nin(SiDnodes);
+ p(SiDnodes) = pin(SiDnodes);
+
+
+ %%%
+ %%% Compute LHS matrices
+ %%%
+
+ %% let's compute FEM approximation of $$ L = - \frac{d^2}{x^2} $$
+ %L = Ucomplap (mesh,ones(Nelements,1));
+
+ %% compute $$ Mv = ( n + p) $$
+ %% and the (lumped) mass matrix M
+ freecarr=zeros(Nnodes,1);
+ freecarr(Sinodes)=(n + p);
+ Mv = freecarr;
+ M = DDGOXNLPOISSON_MASS*spdiag(Mv);
+
+ %%%
+ %%% Compute RHS vector (-residual)
+ %%%
+
+ %% now compute $$ T0 = \frac{q}{\epsilon} (n - p - D) $$
+ totcharge( Sinodes)=(n - p - D);
+ Tv0 = totcharge;
+ T0 = Tv0 .* DDGOXNLPOISSON_RHS;%T0 = Ucompconst (mesh,Tv0,ones(Nelements,1));
+
+ %% now we're ready to build LHS matrix and RHS of the linear system for 1st Newton step
+ A = DDGOXNLPOISSON_LAP + M;
+ R = DDGOXNLPOISSON_LAP * Vnew + T0;
+
+ %% Apply boundary conditions
+ A (Dnodes,:) = [];
+ A (:,Dnodes) = [];
+ R(Dnodes) = [];
+
+ %% compute $$ | R_{k+1} | $$ for the convergence test
+ normrnew= norm(R,inf);
+
+ % check if more damping is needed
+ if (normrnew > normr(newtit))
+ tk = tk/dampcoeff;
+ else
+ if (verbose>0)
+ fprintf(1,'\nexiting damping cycle because residual norm = %e \n-----------\n',normrnew);
+ end
+ break
+ end
+ end
+
+ V = Vnew;
+ normr(newtit+1) = normrnew;
+ dVnorm = norm(tk*dV,inf);
+ pause(.1);
+ % check if convergence has been reached
+ reldVnorm = dVnorm / norm(V,inf);
+ if (reldVnorm <= toll)
+ if(verbose>0)
+ fprintf(1,'\nexiting newton cycle because reldVnorm= %e \n',reldVnorm);
+ end
+ break
+ end
+
+end
+
+res = normr;
+niter = newtit;
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff