2: /*
  3: Laplacian in 3D. Modeled by the partial differential equation

  5:    - Laplacian u = 1,0 < x,y,z < 1,

  7: with boundary conditions

  9:    u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.

 11:    This uses multigrid to solve the linear system

 13:    See src/snes/examples/tutorials/ex50.c

 15:    Can also be run with -pc_type exotic -ksp_type fgmres

 17: */

 19: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";

 21:  #include <petscksp.h>
 22:  #include <petscdm.h>
 23:  #include <petscdmda.h>

 25: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,void*);
 26: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
 27: extern PetscErrorCode ComputeInitialGuess(KSP,Vec,void*);

 29: int main(int argc,char **argv)
 30: {
 32:   KSP            ksp;
 33:   PetscReal      norm;
 34:   DM             da;
 35:   Vec            x,b,r;
 36:   Mat            A;

 38:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 40:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 41:   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);
 42:   DMSetFromOptions(da);
 43:   DMSetUp(da);
 44:   KSPSetDM(ksp,da);
 45:   KSPSetComputeInitialGuess(ksp,ComputeInitialGuess,NULL);
 46:   KSPSetComputeRHS(ksp,ComputeRHS,NULL);
 47:   KSPSetComputeOperators(ksp,ComputeMatrix,NULL);
 48:   DMDestroy(&da);

 50:   KSPSetFromOptions(ksp);
 51:   KSPSolve(ksp,NULL,NULL);
 52:   KSPGetSolution(ksp,&x);
 53:   KSPGetRhs(ksp,&b);
 54:   VecDuplicate(b,&r);
 55:   KSPGetOperators(ksp,&A,NULL);

 57:   MatMult(A,x,r);
 58:   VecAXPY(r,-1.0,b);
 59:   VecNorm(r,NORM_2,&norm);
 60:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",(double)norm);

 62:   VecDestroy(&r);
 63:   KSPDestroy(&ksp);
 64:   PetscFinalize();
 65:   return ierr;
 66: }

 68: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
 69: {
 71:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
 72:   DM             dm;
 73:   PetscScalar    Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
 74:   PetscScalar    ***barray;

 77:   KSPGetDM(ksp,&dm);
 78:   DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
 79:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
 80:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
 81:   DMDAGetCorners(dm,&xs,&ys,&zs,&xm,&ym,&zm);
 82:   DMDAVecGetArray(dm,b,&barray);

 84:   for (k=zs; k<zs+zm; k++) {
 85:     for (j=ys; j<ys+ym; j++) {
 86:       for (i=xs; i<xs+xm; i++) {
 87:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
 88:           barray[k][j][i] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
 89:         } else {
 90:           barray[k][j][i] = Hx*Hy*Hz;
 91:         }
 92:       }
 93:     }
 94:   }
 95:   DMDAVecRestoreArray(dm,b,&barray);
 96:   return(0);
 97: }

 99: PetscErrorCode ComputeInitialGuess(KSP ksp,Vec b,void *ctx)
100: {

104:   VecSet(b,0);
105:   return(0);
106: }

108: PetscErrorCode ComputeMatrix(KSP ksp,Mat jac,Mat B,void *ctx)
109: {
110:   DM             da;
112:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
113:   PetscScalar    v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
114:   MatStencil     row,col[7];

117:   KSPGetDM(ksp,&da);
118:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
119:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
120:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
121:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

123:   for (k=zs; k<zs+zm; k++) {
124:     for (j=ys; j<ys+ym; j++) {
125:       for (i=xs; i<xs+xm; i++) {
126:         row.i = i; row.j = j; row.k = k;
127:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
128:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
129:           MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
130:         } else {
131:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
132:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
133:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
134:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
135:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
136:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
137:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
138:           MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
139:         }
140:       }
141:     }
142:   }
143:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
144:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
145:   return(0);
146: }