Actual source code: ex45.c
petsc-3.3-p2 2012-07-13
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 <petscdmda.h>
24: extern PetscErrorCode ComputeMatrix(KSP,Mat,Mat,MatStructure*,void*);
25: extern PetscErrorCode ComputeRHS(KSP,Vec,void*);
26: extern PetscErrorCode ComputeInitialGuess(DM,Vec);
30: int main(int argc,char **argv)
31: {
33: KSP ksp;
34: PetscReal norm;
35: DM da;
36: Vec x,b,r;
37: Mat A;
39: PetscInitialize(&argc,&argv,(char *)0,help);
41: KSPCreate(PETSC_COMM_WORLD,&ksp);
42: DMDACreate3d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-7,-7,-7,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
43: DMSetInitialGuess(da,ComputeInitialGuess);
44:
45: KSPSetComputeRHS(ksp,ComputeRHS,PETSC_NULL);
46: KSPSetComputeOperators(ksp,ComputeMatrix,PETSC_NULL);
47: KSPSetDM(ksp,da);
48: DMDestroy(&da);
50: KSPSetFromOptions(ksp);
51: KSPSolve(ksp,PETSC_NULL,PETSC_NULL);
52: KSPGetSolution(ksp,&x);
53: KSPGetRhs(ksp,&b);
54: VecDuplicate(b,&r);
55: KSPGetOperators(ksp,&A,PETSC_NULL,PETSC_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",norm);
62: VecDestroy(&r);
63: KSPDestroy(&ksp);
64: PetscFinalize();
66: return 0;
67: }
71: PetscErrorCode ComputeRHS(KSP ksp,Vec b,void *ctx)
72: {
74: PetscInt mx,my,mz;
75: PetscScalar h;
76: DM dm;
79: KSPGetDM(ksp,&dm);
80: DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
81: h = 1.0/((mx-1)*(my-1)*(mz-1));
82: VecSet(b,h);
83: return(0);
84: }
88: PetscErrorCode ComputeInitialGuess(DM dm,Vec b)
89: {
93: VecSet(b,0);
94: return(0);
95: }
99: PetscErrorCode ComputeMatrix(KSP ksp,Mat jac,Mat B,MatStructure *stflg,void *ctx)
100: {
101: DM da;
103: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
104: PetscScalar v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
105: MatStencil row,col[7];
108: KSPGetDM(ksp,&da);
109: DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
110: Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
111: HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
112: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
113:
114: for (k=zs; k<zs+zm; k++){
115: for (j=ys; j<ys+ym; j++){
116: for(i=xs; i<xs+xm; i++){
117: row.i = i; row.j = j; row.k = k;
118: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
119: v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
120: MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
121: } else {
122: v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
123: v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
124: v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
125: v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
126: v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
127: v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
128: v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
129: MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
130: }
131: }
132: }
133: }
134: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
135: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
136: *stflg = SAME_NONZERO_PATTERN;
137: return(0);
138: }