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[Fsem-commits] SF.net SVN: fsem: [118] fsem
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From: <fab...@us...> - 2007-03-06 15:46:06
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Revision: 118
http://fsem.svn.sourceforge.net/fsem/?rev=118&view=rev
Author: fabiandortu
Date: 2007-03-06 07:45:52 -0800 (Tue, 06 Mar 2007)
Log Message:
-----------
Added few scripts in example-fondation to deal with Schwarz decomposition.
This is not used by FSEM since it does not introduce any improvement.
Modified Paths:
--------------
fsem/examples-fondation/schwartz-decomposition/schwarz_varf_1mat_CI.edp
fsem/include-freefem/load.link
fsem/mesh/modules/fsem_Mod_MiscCppModules_Load.edp
Added Paths:
-----------
fsem/examples-fondation/schwartz-decomposition/Helmoltz_anisotrope.edp
fsem/examples-fondation/schwartz-decomposition/P0_P1_comp.edp
fsem/examples-fondation/schwartz-decomposition/non-overlap/
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap.edp
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M.edp
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M_CI.edp
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_2M.edp
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-th.eps
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-u.eps
fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-u0.eps
fsem/examples-fondation/schwartz-decomposition/non-overlap-gc/
fsem/examples-fondation/schwartz-decomposition/non-overlap-gc/schwarz-gc.edp
fsem/examples-fondation/schwartz-decomposition/schwarz2_varf_1mat_CI.edp
Added: fsem/examples-fondation/schwartz-decomposition/Helmoltz_anisotrope.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/Helmoltz_anisotrope.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/Helmoltz_anisotrope.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,124 @@
+// Solve Helmoltz equation on a highly anisotropic mesh
+//
+// - D nabla U + U/tau = source
+//
+// D is the diffusion coefficient (cm2/s)
+// tau is the recombination lifetime (s)
+// source is the generation rate (cm-3 s-1)
+// U is the carrier concentration (cm-3)
+
+//
+// The problem is first solve on a quasi-isotropic mesh.
+// It is then solved on a higly anisotropic mesh.
+//
+
+real Err;
+real scaling = 10;
+
+real Xj = 10.0; // m
+Xj = Xj/scaling;
+
+real Ychar = 1.0 / 1000.0;
+
+real R = 40.0; //m
+real T = 40.0; //m
+real rad = 1.0;
+
+// Mesh definition:
+// The domain is a square but we introduce an inner
+// border at -Xj where the mesh will be strongly refined
+// and will become anisotropic after few adaptmesh (see later)
+border aa(t=0,R){x=t;y=-T;};
+border bb1(t=-T,-Xj){x=R;y=t;};
+border bb2(t=-Xj,0){x=R;y=t;};
+border cc(t=R,0){x=t ;y=0;};
+border dd2(t=0,-Xj){x = 0; y = t;};
+border dd1(t=-Xj,-T){x = 0; y = t;};
+border junc(t=0,R){x=t;y=-Xj;};
+
+int n=4;
+mesh Th = buildmesh( aa(5*n) + bb1(5*n) + bb2(5*n) + cc(5*n) + dd2(5*n) + dd1(5*n)+ junc(5*n));
+plot(Th, wait=0);
+
+fespace Vh(Th, P1); // used for adaptation
+Vh sol;
+int i=0;
+Vh source; // Generation rate
+Vh tau; // Recombination lifetime
+real D=100; // diffusivity
+Vh AdaptFunc;
+
+// generation profile (a gausian laser at x=0)
+macro SourceProfile()
+ (exp(y/T) * exp(-(x/rad)^2))
+// EOM
+
+// used to adapt the mesh around Xj
+macro TauProfile()
+ (exp(-((y+Xj)/(Ychar))^2) + 1)
+// EOM
+
+
+// Helmoltz' equation definition
+varf Kaa(U,V) = int2d(Th)( D*(dx(U)*dx(V)+dy(U)*dy(V)) )
+ +int2d(Th) ( U * V / tau);
+varf laa(U,V) = int2d(Th)( - source * V);
+
+matrix A;
+Vh Fa;
+
+
+// ***************************************
+// **** Solve on quasi isotropic mesh ****
+// ***************************************
+
+// Refines single mesh on generation only
+for ( i=0 ;i< 11; i++) {
+ source = SourceProfile;
+ Err = (0.005 - 0.01)*i/10 + 0.01;
+ Th = adaptmesh(Th, source, err=Err, nbsmooth=5, nbvx=100000, iso=false);
+ plot(Th, wait=0);
+}
+
+source = SourceProfile;
+tau = 1;
+A=Kaa(Vh,Vh);
+Fa = 0; /* reallocate Fa on current mesh */
+Fa[] = laa(0,Vh);
+sol = 0; /* reallocate sol on current mesh */
+sol[]=A^-1*Fa[];
+cout << "Solution on normal mesh:" << endl;
+x=0; y=0;
+cout << "sol(0,0): " << sol << endl;
+plot(sol, wait=true);
+
+
+// *****************************************
+// **** Solve on higly anisotropic mesh ****
+// *****************************************
+
+// Refines single mesh on generation and tau
+for ( i=0 ;i< 11; i++) {
+ source = SourceProfile;
+ tau = TauProfile;
+ AdaptFunc = source + tau;
+ Err = (0.005 - 0.01)*i/10 + 0.01;
+ Th = adaptmesh(Th, AdaptFunc, err=Err, nbsmooth=5, nbvx=100000, iso=false);
+ plot(Th, wait=0);
+}
+
+source = SourceProfile;
+tau = 1;
+A=Kaa(Vh,Vh);
+Fa = 0; /* reallocate Fa on current mesh */
+Fa[] = laa(0,Vh);
+sol = 0; /* reallocate sol on current mesh */
+sol[]=A^-1*Fa[];
+cout << "Solution on normal mesh:" << endl;
+x=0; y=0;
+cout << "Solution on a very anisotropic mesh:" << endl;
+cout << "sol(0,0): " << sol << endl;
+plot(sol, wait=true); // The solution is obviously wrong!!!
+plot(tau, wait=true);
+
+
Added: fsem/examples-fondation/schwartz-decomposition/P0_P1_comp.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/P0_P1_comp.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/P0_P1_comp.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,68 @@
+// Schartz decomposition example on highy anisotropic mesh
+
+real scaling=1.0;
+real Xj = 10.0; // m
+Xj = Xj/scaling;
+real Ychar = 1.0 / 1000.0;
+real R = 40.0; //m
+real T = 40.0; //m
+real rad = 1.0;
+
+// Single mesh (needed for comparison)
+border aa(t=0,R){x=t;y=-T;};
+border bb1(t=-T,0){x=R;y=t;};
+border cc(t=R,0){x=t ;y=0;};
+border dd2(t=0,-T){x = 0; y = t;};
+
+
+int n = 4;
+mesh GloMesh = buildmesh( aa(5*n) + bb1(5*n) + cc(5*n) + dd2(5*n) );
+
+plot(GloMesh, wait=1); // to see the 2 meshes
+
+//The space and problem definition is :
+fespace GloVhP(GloMesh, P2); // used for resolution
+fespace GloVhP1(GloMesh, P1); // used for adaptation
+GloVhP sol; //U,V;
+
+GloVhP source; // Generation rate
+GloVhP1 sourceAdapt;
+
+// generation and recombination lifetime profile
+macro SourceProfile()
+ (exp(y/T) * exp(-(x/rad)^2))
+// EOM
+
+int i;
+real Err;
+// Refines single mesh on generation only
+for ( i=0 ;i< 5; i++) {
+ // refines All
+ sourceAdapt = SourceProfile;
+ Err = (0.001 - 0.01)*i/10 + 0.01;
+ GloMesh = adaptmesh(GloMesh, sourceAdapt, err=Err, nbsmooth=5, nbvx=100000, iso=false);
+ plot(GloMesh, wait=0);
+}
+
+// Classical edp definition
+varf Kaa(U,V) = int2d(GloMesh)( 100*(dx(U)*dx(V)+dy(U)*dy(V)) )
+ +int2d(GloMesh) ( U * V );// + on(back,U= 0 ) ;
+varf laa(U,V) = int2d(GloMesh)( - source * V);
+
+
+matrix A;
+GloVhP Fa;
+
+source = SourceProfile;
+A=Kaa(GloVhP,GloVhP);
+Fa = 0; /* reallocate Fa on current mesh */
+Fa[] = laa(0,GloVhP);
+sol = 0; /* reallocate U on current mesh */
+sol[]=A^-1*Fa[];
+cout << "Solution on normal mesh:" << endl;
+x=0; y=0;
+cout << endl << "U(0,0): " << sol << endl;
+plot(sol, wait=true);
+
+
+
Added: fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,39 @@
+// schwarz1 without overlapping
+int inside = 2;
+int outside = 1;
+border a(t=1,2){x=t;y=0;label=outside;};
+border b(t=0,1){x=2;y=t;label=outside;};
+border c(t=2,0){x=t ;y=1;label=outside;};
+border d(t=1,0){x = 1-t; y = t;label=inside;};
+border e(t=0, 1){ x= 1-t; y = t;label=inside;};
+border e1(t=pi/2, 2*pi){ x= cos(t); y = sin(t);label=outside;};
+int n=4;
+mesh th = buildmesh( a(5*n) + b(5*n) + c(10*n) + d(5*n));
+mesh TH = buildmesh ( e(5*n) + e1(25*n) );
+plot(th,TH,wait=1,ps="schwarz-no-th.eps");
+fespace vh(th,P1);
+fespace VH(TH,P1);
+vh u=0,v; VH U,V;
+vh lambda=0;
+int i=0;
+
+problem PB(U,V,init=i,solver=Cholesky) =
+ int2d(TH)( dx(U)*dx(V)+dy(U)*dy(V) )
+ + int2d(TH)( -V)
+ + int1d(TH,inside)(lambda*V) + on(outside,U= 0 ) ;
+problem pb(u,v,init=i,solver=Cholesky) =
+ int2d(th)( dx(u)*dx(v)+dy(u)*dy(v) )
+ + int2d(th)( -v)
+ + int1d(th,inside)(-lambda*v) + on(outside,u = 0 ) ;
+
+
+for ( i=0 ;i< 10; i++)
+{
+ PB;
+ pb;
+ lambda = lambda - (u-U)/2;
+ if (i==0)
+ plot(U,u,wait=true,ps="schwarz-no-u"+i+".eps");
+};
+
+plot(U,u,ps="schwarz-no-u.eps", wait=1);
Added: fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,64 @@
+// schwarz1 without overlapping
+int inside = 2;
+int outside = 1;
+border a(t=1,2){x=t;y=0;label=outside;};
+border b(t=0,1){x=2;y=t;label=outside;};
+border c(t=2,0){x=t ;y=1;label=outside;};
+border d(t=1,0){x = 1-t; y = t;label=inside;};
+border e(t=0, 1){ x= 1-t; y = t;label=inside;};
+border e1(t=pi/2, 2*pi){ x= cos(t); y = sin(t);label=outside;};
+
+int n=4;
+mesh Tha = buildmesh( a(5*n) + b(5*n) + c(10*n) + d(5*n));
+mesh Thb = buildmesh ( e(5*n) + e1(25*n) );
+mesh Th = Tha;
+
+plot(Tha,Thb,wait=1,ps="schwarz-no-th.eps");
+
+
+fespace Vh(Th,P1);
+
+Vh sol=0, solPrev;
+Vh lambda=0;
+Vh lambdaX=0;
+int i=0;
+
+varf Ka(U,V,init=i,solver=Cholesky) =
+int2d(Th)( dx(U)*dx(V)+dy(U)*dy(V) )+ on(outside,U= 0 ) ;
+// + int2d(Th)( -U*V) ;
+
+varf La(U,V)= -int2d(Th)( -V)
+ - int1d(Th,inside)(lambdaX*V) + on(outside,U= 0 ) ;
+
+
+macro SolveProblem()
+ A=Ka(Vh,Vh);
+ Fa = 0; /* reallocate Fa on current mesh */
+ Fa[] = La(0,Vh);
+ sol = 0; /* reallocate U on current mesh */
+ sol[]=A^-1*Fa[];
+// EOM
+
+matrix A;
+Vh Fa;
+
+for ( i=0 ;i< 10; i++)
+{
+ solPrev = sol;
+ Th = Tha;
+ lambdaX = +lambda;
+ SolveProblem;
+
+ solPrev = sol;
+ lambdaX = -lambda;
+ Th = Thb;
+ SolveProblem;
+
+ lambda = lambda - (sol-solPrev)/2;
+
+ if (i==0)
+ plot(solPrev,sol,wait=true,ps="schwarz-no-u"+i+".eps");
+ //plot(solPrev, sol, wait=true);
+};
+
+plot(solPrev,sol,ps="schwarz-no-u.eps", wait=1);
Added: fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M_CI.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M_CI.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_1M_CI.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,159 @@
+// schwarz1 without overlapping
+int inside = 2; // inside boundary
+int outside = 1; // outside boundary
+int junction =3;
+int back = 4;
+
+
+/* TOTAL domain top substrate
+ *
+ * 0 R 0 R 0 R
+ * 0 |-----------| 0 |----c-----|
+ * | | | |
+ * | | d b
+ * | | | |
+ * -Xj |___________| -Xj |_____a____| -Xj _____g_____
+ * | | | |
+ * | | | |
+ * | | h f
+ * | | | |
+ * -T |-----------| -T |----e----|
+ *
+ */
+
+
+real Err;
+real scaling = 10;
+
+real Xj = 10.0; // m
+Xj = Xj/scaling;
+real dx1 = 2.0;
+dx1 = dx1/scaling; // m
+real dx2 = 4.0;
+dx2 = dx2/scaling; // m
+
+real Ychar = 1.0 / 1000.0;
+real R = 40.0; //m
+real T = 40.0; //m
+real rad = 1.0;
+
+// top layer (very thin, 100 nm = 1e-7 m)
+border a(t=0,R){x=t;y=-Xj;label=inside;};
+border b(t=-Xj,0){x=R;y=t;label=outside;};
+border c(t=R,0){x=t ;y=0;label=outside;};
+border d(t=0,-Xj){x = 0; y = t;label=outside;};
+
+
+// bottom layer (very thick, 600 um = 6e-4 m)
+border e(t=0, R){ x= t; y = -T;label=back;};
+border f(t=-T, -Xj){ x= R; y = t;label=outside;};
+border g(t=R, 0){ x= t; y = -Xj;label=inside;};
+border h(t=-Xj, -T){ x= 0; y = t;label=outside;};
+
+int n=4;
+mesh topTh = buildmesh( a(5*n) + b(5*n) + c(5*n) + d(5*n));
+mesh botTh = buildmesh( e(5*n) + f(5*n) + g(5*n) + h(5*n));
+
+mesh Th = topTh;
+
+plot(topTh,botTh,wait=1,ps="schwarz-no-th.eps");
+
+
+fespace Vh(Th,P1);
+
+real D=100; // diffusivity
+Vh sol=0, solPrev;
+Vh lambda=0;
+Vh lambdaX=0;
+Vh source, tau;
+Vh AdaptFunc;
+int i=0;
+
+// generation and recombination lifetime profile
+macro SourceProfile()
+ (exp(y/T) * exp(-(x/rad)^2))
+// EOM
+
+macro TauProfile()
+ (exp(-((y)/(Ychar))^2) + 1)
+// EOM
+
+macro TauProfile2()
+ (-y^2/Xj)
+// EOM
+
+// Refines dual mesh
+for ( i=0 ;i< 11; i++) {
+ Err = (0.001 - 0.01)*i/10 + 0.01;
+
+ // refines top
+ Th = topTh;
+ source = SourceProfile;
+ tau = TauProfile2;
+ AdaptFunc = source + tau;
+ topTh = adaptmesh(topTh, AdaptFunc, err=Err, nbsmooth=5, nbvx=100000, iso=false);
+ plot(AdaptFunc, wait=1);
+
+ Err = (0.005 - 0.01)*i/10 + 0.01;
+ // refines bottom
+ Th = botTh;
+ source = SourceProfile;
+ tau = 1;
+ AdaptFunc = source + tau;
+ //AdaptFunc = source + Tau;
+ botTh = adaptmesh(botTh, AdaptFunc, err=Err, nbsmooth=5, nbvx=100000, iso=false);
+ plot(AdaptFunc, wait=0);
+
+ plot(topTh, botTh, wait=0);
+
+}
+
+
+// **********************************************************
+// **********************************************************
+// **********************************************************
+varf Ka(U,V,init=i,solver=Cholesky) =
+int2d(Th)( D*(dx(U)*dx(V)+dy(U)*dy(V)) )
+ + int2d(Th) (U*V); //+ on(outside,U= 0 ) ;
+// + int2d(Th)( -U*V) ;
+
+varf La(U,V)= -int2d(Th)( -source * V)
+ - int1d(Th,inside)(lambdaX*V); //+ on(outside,U= 0 ) ;
+
+
+macro SolveProblem()
+ A=Ka(Vh,Vh);
+ Fa = 0; /* reallocate Fa on current mesh */
+ Fa[] = La(0,Vh);
+ sol = 0; /* reallocate U on current mesh */
+ sol[]=A^-1*Fa[];
+// EOM
+
+matrix A;
+Vh Fa;
+
+tau =1;
+
+for ( i=0 ;i< 300; i++)
+{
+ solPrev = sol;
+ Th = topTh;
+ source = SourceProfile;
+ lambdaX = +lambda;
+ SolveProblem;
+
+ solPrev = sol;
+ Th = botTh;
+ lambdaX = -lambda;
+ source = SourceProfile;
+ SolveProblem;
+
+ lambda = lambda - (sol-solPrev)/2;
+ cout << "lambda: " << lambda[].max << ", " << lambda[].min << endl;
+ if (i==0)
+ plot(solPrev,sol,wait=true,ps="schwarz-no-u"+i+".eps");
+ plot(solPrev, sol, wait=false);
+};
+
+plot(solPrev,sol,ps="schwarz-no-u.eps", wait=1);
+plot(solPrev,sol,ps="schwarz-no-u.eps", wait=1);
Added: fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_2M.edp
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_2M.edp (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-overlap_2M.edp 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,52 @@
+// schwarz1 without overlapping
+
+int inside = 2;
+int outside = 1;
+border a(t=1,2){x=t;y=0;label=outside;};
+border b(t=0,1){x=2;y=t;label=outside;};
+border c(t=2,0){x=t ;y=1;label=outside;};
+border d(t=1,0){x = 1-t; y = t;label=inside;};
+border e(t=0, 1){ x= 1-t; y = t;label=inside;};
+border e1(t=pi/2, 2*pi){ x= cos(t); y = sin(t);label=outside;};
+int n=4;
+mesh th = buildmesh( a(5*n) + b(5*n) + c(10*n) + d(5*n));
+mesh TH = buildmesh ( e(5*n) + e1(25*n) );
+plot(th,TH,wait=1,ps="schwarz-no-th.eps");
+fespace vh(th,P1);
+fespace VH(TH,P1);
+vh u=0; VH U;
+vh lambda=0;
+int i=0;
+
+varf PB(U,V,init=i,solver=Cholesky) =
+ int2d(TH)( dx(U)*dx(V)+dy(U)*dy(V) ) + on(outside,U= 0 ) ;
+varf LB(U,V) = -int2d(TH)( -V)
+ - int1d(TH,inside)(lambda*V) + on(outside,U= 0 ) ;
+
+varf pb(u,v,init=i,solver=Cholesky) =
+ int2d(th)( dx(u)*dx(v)+dy(u)*dy(v) ) + on(outside,u = 0 ) ;
+varf lb(u,v) = -int2d(th)( -v)
+ - int1d(th,inside)(-lambda*v) +on(outside,u = 0 ) ;
+
+matrix A;
+VH FB;
+vh fb;
+
+for ( i=0 ;i< 10; i++)
+{
+ A = PB(VH, VH);
+ FB = 0;
+ FB[] = LB(0,VH);
+ U[] = A^-1*FB[];
+
+ A = pb(vh, vh);
+ fb = 0;
+ fb[] = lb(0,vh);
+ u[] = A^-1*fb[];
+
+ lambda = lambda - (u-U)/2;
+ if (i==0)
+ plot(U,u,wait=true,ps="schwarz-no-u"+i+".eps");
+};
+
+plot(U,u,ps="schwarz-no-u.eps", wait=1);
Added: fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-th.eps
===================================================================
--- fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-th.eps (rev 0)
+++ fsem/examples-fondation/schwartz-decomposition/non-overlap/schwarz-no-th.eps 2007-03-06 15:45:52 UTC (rev 118)
@@ -0,0 +1,3810 @@
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