Actual source code: ex22.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 multigrid to solve the linear system
13: */
15: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";
17: #include petscda.h
18: #include petscksp.h
19: #include petscdmmg.h
26: int main(int argc,char **argv)
27: {
29: DMMG *dmmg;
30: PetscReal norm;
31: DA da;
33: PetscInitialize(&argc,&argv,(char *)0,help);
35: DMMGCreate(PETSC_COMM_WORLD,3,PETSC_NULL,&dmmg);
36: DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-3,-3,-3,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
37: DMMGSetDM(dmmg,(DM)da);
38: DADestroy(da);
40: DMMGSetKSP(dmmg,ComputeRHS,ComputeMatrix);
42: DMMGSetUp(dmmg);
43: DMMGSolve(dmmg);
45: MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
46: VecAXPY(DMMGGetr(dmmg),-1.0,DMMGGetRHS(dmmg));
47: VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
48: /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm); */
50: DMMGDestroy(dmmg);
51: PetscFinalize();
53: return 0;
54: }
58: PetscErrorCode ComputeRHS(DMMG dmmg,Vec b)
59: {
61: PetscInt mx,my,mz;
62: PetscScalar h;
65: DAGetInfo((DA)dmmg->dm,0,&mx,&my,&mz,0,0,0,0,0,0,0);
66: h = 1.0/((mx-1)*(my-1)*(mz-1));
67: VecSet(b,h);
68: return(0);
69: }
70:
73: PetscErrorCode ComputeMatrix(DMMG dmmg,Mat jac,Mat B)
74: {
75: DA da = (DA)dmmg->dm;
77: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
78: PetscScalar v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
79: MatStencil row,col[7];
81: DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);
82: Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
83: HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
84: DAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
85:
86: for (k=zs; k<zs+zm; k++){
87: for (j=ys; j<ys+ym; j++){
88: for(i=xs; i<xs+xm; i++){
89: row.i = i; row.j = j; row.k = k;
90: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
91: v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
92: MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
93: } else {
94: v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
95: v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
96: v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
97: v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
98: v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
99: v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
100: v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
101: MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
102: }
103: }
104: }
105: }
106: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
107: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
108: return 0;
109: }