Actual source code: ex42.c

  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 2 level multigrid with the wirebasket based coarse problem to solve the linear system

 13: */

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

 17:  #include petscda.h
 18:  #include petscksp.h
 19:  #include petscmg.h


 27: int main(int argc,char **argv)
 28: {
 30:   KSP            ksp;
 31:   PC             pc;
 32:   Vec            x,b;
 33:   DA             da;
 34:   Mat            A;

 36:   PetscInitialize(&argc,&argv,(char *)0,help);

 38:   DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-8,-8,-8,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
 39:   DACreateGlobalVector(da,&x);
 40:   DACreateGlobalVector(da,&b);
 41:   ComputeRHS(da,b);
 42:   DAGetMatrix(da,MATAIJ,&A);
 43:   ComputeMatrix(da,A);

 45:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 46:   KSPSetFromOptions(ksp);
 47:   KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);
 48:   KSPGetPC(ksp,&pc);
 49:   PCExoticSetDA(pc,da);
 50: 
 51:   KSPSolve(ksp,b,x);
 52: 
 53:   KSPDestroy(ksp);
 54:   VecDestroy(x);
 55:   VecDestroy(b);
 56:   MatDestroy(A);
 57:   DADestroy(da);
 58:   PetscFinalize();

 60:   return 0;
 61: }

 65: PetscErrorCode ComputeRHS(DA da,Vec b)
 66: {
 68:   PetscInt       mx,my,mz;
 69:   PetscScalar    h;

 72:   DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);
 73:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
 74:   VecSet(b,h);
 75:   return(0);
 76: }
 77: 
 80: PetscErrorCode ComputeMatrix(DA da,Mat B)
 81: {
 83:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
 84:   PetscScalar    v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
 85:   MatStencil     row,col[7];

 87:   DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);
 88:   Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
 89:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
 90:   DAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
 91: 
 92:   for (k=zs; k<zs+zm; k++){
 93:     for (j=ys; j<ys+ym; j++){
 94:       for(i=xs; i<xs+xm; i++){
 95:         row.i = i; row.j = j; row.k = k;
 96:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
 97:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
 98:           MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
 99:         } else {
100:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
101:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
102:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
103:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
104:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
105:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
106:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
107:           MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
108:         }
109:       }
110:     }
111:   }
112:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
113:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
114:   return 0;
115: }


121: PetscErrorCode ComputeInterpolation(PC pc,void *ida)
122: {
124:   DA             da = (DA)ida;
125:   Mat            A,P;

128:   PCGetOperators(pc,PETSC_NULL,&A,PETSC_NULL);
129:   DAGetWireBasketInterpolation(da,A,MAT_INITIAL_MATRIX,&P);
130:   PCMGSetInterpolation(pc,1,P);
131:   MatDestroy(P);

133:   return(0);
134: }