--- /dev/null
+
+// /home/couturie/work/petsc-3.5.1/arch-linux2-c-debug/bin/mpirun -np 3 ./ex45 -da_grid_x 160 -da_grid_y 160 -da_grid_z 160 -ksp_type fgmres
+
+
+/*
+Laplacian in 3D. Modeled by the partial differential equation
+
+ - Laplacian u = 1,0 < x,y,z < 1,
+
+with boundary conditions
+
+ u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
+
+ This uses multigrid to solve the linear system
+
+ See src/snes/examples/tutorials/ex50.c
+
+ Can also be run with -pc_type exotic -ksp_type fgmres
+
+*/
+
+static char help[] = "Solves 3D Laplacian using multigrid.\n\n";
+
+#include <petscksp.h>
+#include <petscdm.h>
+#include <petscdmda.h>
+
+extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
+extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
+extern PetscErrorCode ComputeInitialGuess(KSP,Vec,void*);
+
+#undef __FUNCT__
+#define __FUNCT__ "main"
+
+
+
+
+
+
+
+int KrylovMinimize(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar gamma, alpha, oldgamma, beta;
+ PetscReal norm=20, Eprecision=5e-5, cgprec=1e-40;
+ PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=15, Iiter=0;
+ PetscErrorCode ierr;
+ PetscScalar T1, T2;
+ KSP ksp;
+ PetscInt total=0;
+ PetscInt size;
+ PetscInt Istart,Iend;
+ PetscInt i,its;
+ Vec x_old, residu;
+ Mat S, AS;
+ PetscScalar *array;
+ PetscInt *ind_row;
+ Vec Alpha, p, ss, vect, r, q, Ax;
+
+
+ PetscInt first=1;
+
+ ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+ ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
+ ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
+
+
+
+
+ VecGetSize(b,&size);
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Size of vector %D\n", size); CHKERRQ(ierr);
+
+ PetscInt aa,bb;
+ MatGetOwnershipRange(A,&aa,&bb);
+
+ // ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD, "%D %D\n", aa,bb); CHKERRQ(ierr);
+ //PetscSynchronizedFlush(PETSC_COMM_WORLD);
+
+
+ ierr = MatCreate(PETSC_COMM_WORLD, &S);CHKERRQ(ierr);
+ ierr = MatSetSizes(S, bb-aa, PETSC_DECIDE, size, ColS); CHKERRQ(ierr);
+ ierr = MatSetType(S, MATMPIDENSE); CHKERRQ(ierr);
+ ierr = MatSetUp(S); CHKERRQ(ierr);
+
+ ierr = MatGetOwnershipRange(S, &Istart, &Iend); CHKERRQ(ierr);
+
+ ierr = VecCreate(PETSC_COMM_WORLD, &Alpha); CHKERRQ(ierr);
+ ierr = VecSetSizes(Alpha, PETSC_DECIDE, ColS); CHKERRQ(ierr);
+ ierr = VecSetFromOptions(Alpha); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &vect); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &p); CHKERRQ(ierr);
+ ierr = VecDuplicate(Alpha, &ss); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &r); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &q); CHKERRQ(ierr);
+ ierr = VecDuplicate(b, &Ax); CHKERRQ(ierr);
+
+ ierr = VecDuplicate(b,&x_old);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&residu);CHKERRQ(ierr);
+
+
+
+ //indexes of row (these indexes are global)
+ ind_row = (PetscInt*)malloc(sizeof(PetscInt)*(Iend-Istart));
+ for(i=0; i<Iend-Istart; i++) ind_row[i] = i + Istart;
+
+ //Initializations
+ // ierr = KSPGMRESSetRestart(ksp, 16); CHKERRQ(ierr);
+ ierr = KSPSetTolerances(ksp, 1e-10, 1e-10, PETSC_DEFAULT, 16); CHKERRQ(ierr);
+ ierr = KSPSetInitialGuessNonzero(ksp, PETSC_TRUE); CHKERRQ(ierr);
+
+
+
+ //GMRES WITH MINIMIZATION
+ T1 = MPI_Wtime();
+ while(giter<Emaxiter && norm>Eprecision ){
+ for(col=0; col<ColS && norm>Eprecision; col++){
+
+
+ //Solve
+ ierr = KSPSolve(ksp, b, x); CHKERRQ(ierr);
+
+ ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
+ total += its; Iiter ++;
+
+
+
+ //Build S'
+ ierr = VecGetArray(x, &array);
+ ierr = MatSetValues(S, Iend-Istart, ind_row, 1, &col, array, INSERT_VALUES);
+ VecRestoreArray(x, &array);
+
+
+
+ //Error
+ ierr = VecCopy(x, residu); CHKERRQ(ierr);
+ ierr = VecAXPY(residu, -1, x_old); CHKERRQ(ierr);
+ ierr = VecNorm(residu, NORM_INFINITY, &norm); CHKERRQ(ierr);
+
+
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, outer iteration %D\n", norm, giter); CHKERRQ(ierr);
+ ierr = VecCopy(x, x_old); CHKERRQ(ierr);
+
+
+ }
+
+
+ //minimization step
+ if( norm>Eprecision) {
+
+ MatAssemblyBegin(S, MAT_FINAL_ASSEMBLY);
+ MatAssemblyEnd(S, MAT_FINAL_ASSEMBLY);
+
+
+ //Build AS
+ if(first) {
+ MatMatMult(A,S, MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AS);
+ first=0;
+ }
+ else
+ MatMatMult(A,S, MAT_REUSE_MATRIX,PETSC_DEFAULT,&AS);
+
+
+
+
+ //Minimization with CGLS
+ MatMult(AS, Alpha, r); VecAYPX(r, -1, b); //r_0 = b-AS*x_0
+
+
+ MatMultTranspose(AS, r, p); //p_0 = AS'*r_0
+
+
+
+
+ ierr = VecCopy(p, ss); CHKERRQ(ierr); //p_0 = s_0
+ VecNorm(ss, NORM_2, &gamma); gamma = gamma * gamma; //gamma = norm2(s)^2
+ while(gamma>cgprec && iter<iterations){
+ MatMult(AS, p, q); //q = AS*p
+ VecNorm(q, NORM_2, &alpha); alpha = alpha * alpha; //alpha = norm2(q)^2
+ alpha = gamma / alpha;
+ VecAXPY(Alpha, alpha, p); //Alpha += alpha*p
+ VecAXPY(r, -alpha, q); //r -= alpha*q
+ MatMultTranspose(AS, r, ss); // ss = AS'*r
+ oldgamma = gamma;
+ VecNorm(ss, NORM_2, &gamma); gamma = gamma * gamma; //gamma = norm2(s)^2
+ beta = gamma / oldgamma;
+ VecAYPX(p, beta, ss); //p = s+beta*p;
+ iter ++;
+ }
+
+ iter = 0; giter ++;
+ //Minimizer
+ MatMult(S, Alpha, x); //x = S*Alpha;
+ }
+
+ }
+ T2 = MPI_Wtime();
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time : %g (s)\n", T2-T1); CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations : %D\n", total); CHKERRQ(ierr);
+
+ return 0;
+
+}
+
+
+
+
+
+
+
+
+
+int KrylovMinimizeLSQR(Mat A, Vec b, Vec x) {
+
+
+ //Variables
+
+ PetscScalar alpha, beta;
+ PetscReal norm=20, Eprecision=5e-5, tol=1e-40;
+ PetscInt giter=0, ColS=12, col=0, Emaxiter=50000000, iter=0, iterations=15, Iiter=0;
+ PetscErrorCode ierr;
+ PetscScalar T1, T2;
+ KSP ksp;
+ PetscInt total=0;
+ PetscInt size;
+ PetscInt Istart,Iend;
+ PetscInt i,its;
+ Vec x_old, residu;
+ Mat S, AS;
+ PetscScalar *array;
+ PetscInt *ind_row;
+ Vec Ax;
+ PetscScalar norm_ksp;
+ Vec u,v,d,uu,vt,zero_long,zero_short,x_lsqr;
+
+ PetscInt first=1;
+
+ ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+ ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
+ ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
+
+
+
+
+ VecGetSize(b,&size);
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Size of vector %D\n", size); CHKERRQ(ierr);
+
+ PetscInt aa,bb;
+ MatGetOwnershipRange(A,&aa,&bb);
+
+ // ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD, "%D %D\n", aa,bb); CHKERRQ(ierr);
+ //PetscSynchronizedFlush(PETSC_COMM_WORLD);
+
+
+ ierr = MatCreate(PETSC_COMM_WORLD, &S);CHKERRQ(ierr);
+ ierr = MatSetSizes(S, bb-aa, PETSC_DECIDE, size, ColS); CHKERRQ(ierr);
+ ierr = MatSetType(S, MATMPIDENSE); CHKERRQ(ierr);
+ ierr = MatSetUp(S); CHKERRQ(ierr);
+
+ ierr = MatGetOwnershipRange(S, &Istart, &Iend); CHKERRQ(ierr);
+
+
+
+ ierr = VecDuplicate(b, &Ax); CHKERRQ(ierr);
+
+ ierr = VecDuplicate(b,&x_old);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&residu);CHKERRQ(ierr);
+
+
+ //long vector
+ ierr = VecDuplicate(b,&u);CHKERRQ(ierr);
+
+
+ ierr = VecDuplicate(b,&uu);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&zero_long);CHKERRQ(ierr);
+ ierr = VecSet(zero_long,0);CHKERRQ(ierr);
+
+ //small vector
+ ierr = VecCreate(PETSC_COMM_WORLD, &v); CHKERRQ(ierr);
+ ierr = VecSetSizes(v, PETSC_DECIDE, ColS); CHKERRQ(ierr);
+ ierr = VecSetFromOptions(v); CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&zero_short);CHKERRQ(ierr);
+ ierr = VecSet(zero_short,0);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&d);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&vt);CHKERRQ(ierr);
+ ierr = VecDuplicate(v,&x_lsqr);CHKERRQ(ierr);
+
+
+ //indexes of row (these indexes are global)
+ ind_row = (PetscInt*)malloc(sizeof(PetscInt)*(Iend-Istart));
+ for(i=0; i<Iend-Istart; i++) ind_row[i] = i + Istart;
+
+ //Initializations
+ // ierr = KSPGMRESSetRestart(ksp, 16); CHKERRQ(ierr);
+ ierr = KSPSetTolerances(ksp, 1e-10, 1e-10, PETSC_DEFAULT, 16); CHKERRQ(ierr);
+ ierr = KSPSetInitialGuessNonzero(ksp, PETSC_TRUE); CHKERRQ(ierr);
+
+
+
+
+ //GMRES WITH MINIMIZATION
+ T1 = MPI_Wtime();
+ while(giter<Emaxiter && norm>Eprecision ){
+ for(col=0; col<ColS && norm>Eprecision; col++){
+
+
+ //Solve
+ ierr = KSPSolve(ksp, b, x); CHKERRQ(ierr);
+
+ ierr = KSPGetIterationNumber(ksp, &its); CHKERRQ(ierr);
+ total += its; Iiter ++;
+
+
+
+ //Build S'
+ ierr = VecGetArray(x, &array);
+ ierr = MatSetValues(S, Iend-Istart, ind_row, 1, &col, array, INSERT_VALUES);
+ VecRestoreArray(x, &array);
+
+
+
+ //Error
+ ierr = VecCopy(x, residu); CHKERRQ(ierr);
+ ierr = VecAXPY(residu, -1, x_old); CHKERRQ(ierr);
+ ierr = VecNorm(residu, NORM_INFINITY, &norm); CHKERRQ(ierr);
+
+
+
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, outer iteration %D\n", norm, giter); CHKERRQ(ierr);
+ ierr = VecCopy(x, x_old); CHKERRQ(ierr);
+
+
+ }
+
+
+ //minimization step
+ if( norm>Eprecision) {
+
+ MatAssemblyBegin(S, MAT_FINAL_ASSEMBLY);
+ MatAssemblyEnd(S, MAT_FINAL_ASSEMBLY);
+
+
+
+
+ //Build AS
+ if(first) {
+ MatMatMult(A,S, MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AS);
+
+ first=0;
+ }
+ else
+ MatMatMult(A,S, MAT_REUSE_MATRIX,PETSC_DEFAULT,&AS);
+
+
+
+
+
+ //LSQR
+ //LSQR
+ //LSQR
+
+
+
+ PetscScalar n2b,tolb,normr,c,s,phibar,normar,norma,thet,rhot,rho,phi;
+ PetscInt stag;
+ tolb = tol * n2b;
+ VecNorm(b, NORM_2, &n2b); //n2b = norm(b);
+ ierr = VecCopy(b, u); CHKERRQ(ierr); //u=b
+ VecNorm(u, NORM_2, &beta); // beta=norm(u)
+ normr=beta;
+ if (beta != 0) {
+ VecAYPX(u,1/beta,zero_long); // u = u / beta;
+ }
+ c=1;
+ s=0;
+ phibar=beta;
+ MatMultTranspose(AS, u, v); //v=A'*u
+ ierr = VecSet(x_lsqr,0);CHKERRQ(ierr);
+ VecNorm(v, NORM_2, &alpha); // alpha=norm(v)
+ if (alpha != 0) {
+ VecAYPX(v,1/alpha,zero_short); // v = v / alpha;
+ }
+ ierr = VecSet(d,0);CHKERRQ(ierr);
+ normar = alpha * beta;
+ norma=0;
+ //stag=0;
+ for(i=0;i<iterations;i++) {
+ MatMult(AS, v, uu); //uu=A*v
+ VecAYPX(u, -alpha, uu); //u = uu-alpha*u;
+ VecNorm(u, NORM_2, &beta); // beta=norm(u)
+ VecAYPX(u,1/beta,zero_long); // u = u / beta;
+ norma=sqrt(norma*norma+alpha*alpha+beta*beta); // norma = norm([norma alpha beta]);
+ thet = - s * alpha;
+ rhot = c * alpha;
+ rho = sqrt(rhot*rhot + beta*beta);
+ c = rhot / rho;
+ s = - beta / rho;
+ phi = c * phibar;
+ if (phi == 0) { // stagnation of the method
+ stag = 1;
+ }
+ phibar = s * phibar;
+ VecAYPX(d,-thet,v); //d = (v - thet * d);
+ VecAYPX(d,1/rho,zero_short); //d=d/ rho;
+
+
+ if (normar/(norma*normr) <= tol) { // check for convergence in min{|b-A*x|}
+ break;
+ }
+ if (normr <= tolb) { // check for convergence in A*x=b
+ break;
+ }
+
+
+ VecAXPY(x_lsqr,phi,d); // x_lsqr=x_lsqr+phi*d
+ normr = abs(s) * normr;
+ MatMultTranspose(AS, u, vt); //vt=A'*u;
+ VecAYPX(v,-beta,vt); // v = vt - beta * v;
+ VecNorm(v, NORM_2, &alpha); // alpha=norm(v)
+ VecAYPX(v,1/alpha,zero_short); // v = v / alpha;
+ normar = alpha * abs( s * phi);
+ }
+
+
+
+ iter = 0; giter ++;
+ //Minimizer
+ MatMult(S, x_lsqr, x); //x = S*x_small;
+ }
+
+ }
+ T2 = MPI_Wtime();
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time LSQR : %g (s)\n", T2-T1); CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations LSQR : %D\n", total); CHKERRQ(ierr);
+
+ return 0;
+
+}
+
+
+
+
+
+
+
+int main(int argc,char **argv)
+{
+ PetscErrorCode ierr;
+ KSP ksp;
+ PetscReal norm;
+ DM da;
+ Vec x,b,r;
+ Mat A;
+ PetscInt total;
+ PetscScalar T1,T2;
+
+ PetscInitialize(&argc,&argv,(char*)0,help);
+
+ ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
+ ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-7,-7,-7,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);CHKERRQ(ierr);
+ ierr = KSPSetDM(ksp,da);CHKERRQ(ierr);
+ ierr = KSPSetComputeInitialGuess(ksp,ComputeInitialGuess,NULL);CHKERRQ(ierr);
+ ierr = KSPSetComputeRHS(ksp,ComputeRHS,NULL);CHKERRQ(ierr);
+ ierr = KSPSetComputeOperators(ksp,ComputeMatrix,NULL);CHKERRQ(ierr);
+ ierr = DMDestroy(&da);CHKERRQ(ierr);
+
+ ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
+
+
+ ierr = KSPSetTolerances(ksp, 1e-7, 1e-7, PETSC_DEFAULT, 50000000); CHKERRQ(ierr);
+ T1 = MPI_Wtime();
+ ierr = KSPSolve(ksp,NULL,NULL);CHKERRQ(ierr);
+ T2 = MPI_Wtime();
+
+
+
+ ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
+ ierr = KSPGetRhs(ksp,&b);CHKERRQ(ierr);
+ ierr = VecDuplicate(b,&r);CHKERRQ(ierr);
+ ierr = KSPGetOperators(ksp,&A,NULL);CHKERRQ(ierr);
+
+ ierr = MatMult(A,x,r);CHKERRQ(ierr);
+ ierr = VecAXPY(r,-1.0,b);CHKERRQ(ierr);
+ ierr = VecNorm(r,NORM_2,&norm);CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Execution time : %g (s)\n", T2-T1); CHKERRQ(ierr);
+
+ ierr = KSPGetIterationNumber(ksp, &total); CHKERRQ(ierr);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "\t\t\t -- Total number of iterations : %D\n", total); CHKERRQ(ierr);
+
+
+
+ // ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
+
+
+{
+
+ Vec x;
+ Vec sol;
+ VecDuplicate(b,&x);
+ VecDuplicate(b,&sol);
+
+ KrylovMinimize(A, b, x);
+
+
+
+ MatMult(A,x,sol);
+
+
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Error2 %g\n",norm);
+
+ ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
+
+ }
+
+
+ {
+
+ Vec x;
+ Vec sol;
+ VecDuplicate(b,&x);
+ VecDuplicate(b,&sol);
+
+ KrylovMinimizeLSQR(A, b, x);
+
+
+
+ MatMult(A,x,sol);
+
+
+ VecAXPY(sol,-1,b);
+ VecNorm(sol, NORM_2, &norm);
+ ierr = PetscPrintf(PETSC_COMM_WORLD, "Error LSQR %g\n",norm);
+
+
+ ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
+ }
+
+
+ ierr = VecDestroy(&r);CHKERRQ(ierr);
+
+ ierr = PetscFinalize();
+
+ return 0;
+}
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeRHS"
+PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
+{
+ PetscErrorCode ierr;
+ PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
+ DM dm;
+ PetscScalar Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
+ PetscScalar ***barray;
+
+ PetscFunctionBeginUser;
+ ierr = KSPGetDM(ksp,&dm);CHKERRQ(ierr);
+ ierr = DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
+ Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
+ HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
+ ierr = DMDAGetCorners(dm,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
+ ierr = DMDAVecGetArray(dm,b,&barray);CHKERRQ(ierr);
+
+ for (k=zs; k<zs+zm; k++) {
+ for (j=ys; j<ys+ym; j++) {
+ for (i=xs; i<xs+xm; i++) {
+ if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
+ barray[k][j][i] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
+ } else {
+ barray[k][j][i] = Hx*Hy*Hz;
+ }
+ }
+ }
+ }
+ ierr = DMDAVecRestoreArray(dm,b,&barray);CHKERRQ(ierr);
+ PetscFunctionReturn(0);
+}
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeInitialGuess"
+PetscErrorCode ComputeInitialGuess(KSP ksp,Vec b,void *ctx)
+{
+ PetscErrorCode ierr;
+
+ PetscFunctionBeginUser;
+ ierr = VecSet(b,0);CHKERRQ(ierr);
+ PetscFunctionReturn(0);
+}
+
+#undef __FUNCT__
+#define __FUNCT__ "ComputeMatrix"
+PetscErrorCode ComputeMatrix(KSP ksp,Mat jac,Mat B,void *ctx)
+{
+ DM da;
+ PetscErrorCode ierr;
+ PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
+ PetscScalar v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
+ MatStencil row,col[7];
+
+ PetscFunctionBeginUser;
+ ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
+ ierr = DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
+ Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
+ HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
+ ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
+
+ for (k=zs; k<zs+zm; k++) {
+ for (j=ys; j<ys+ym; j++) {
+ for (i=xs; i<xs+xm; i++) {
+ row.i = i; row.j = j; row.k = k;
+ if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
+ v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
+ ierr = MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
+ } else {
+ v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
+ v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
+ v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
+ v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
+ v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
+ v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
+ v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
+ ierr = MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);CHKERRQ(ierr);
+ }
+ }
+ }
+ }
+ ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+ ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
+ PetscFunctionReturn(0);
+}
