Actual source code: ex22.c
2: /*
3: THIS EXAMPLE IS DEPRECATED, USE ex45.c
4: */
7: /*
8: Laplacian in 3D. Modeled by the partial differential equation
10: - Laplacian u = 1,0 < x,y,z < 1,
12: with boundary conditions
14: u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
16: This uses multigrid to solve the linear system
18: */
20: static char help[] = "Solves 3D Laplacian using multigrid.\n\n";
22: #include <petscdmda.h>
23: #include <petscksp.h>
24: #include <petscdmmg.h>
31: int main(int argc,char **argv)
32: {
34: DMMG *dmmg;
35: PetscReal norm;
36: PetscInt nlevels = 3;
37: DM da;
39: PetscInitialize(&argc,&argv,(char *)0,help);
40: PetscOptionsGetInt(PETSC_NULL,"-nlevels",&nlevels,PETSC_NULL);
41: DMMGCreate(PETSC_COMM_WORLD,nlevels,PETSC_NULL,&dmmg);
42: DMDACreate3d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-3,-3,-3,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
43: DMMGSetDM(dmmg,(DM)da);
44: DMDestroy(&da);
46: DMMGSetKSP(dmmg,ComputeRHS,ComputeMatrix);
48: DMMGSolve(dmmg);
50: MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
51: VecAXPY(DMMGGetr(dmmg),-1.0,DMMGGetRHS(dmmg));
52: VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
53: /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm); */
55: DMMGDestroy(dmmg);
56: PetscFinalize();
58: return 0;
59: }
63: PetscErrorCode ComputeRHS(DMMG dmmg,Vec b)
64: {
66: PetscInt mx,my,mz;
67: PetscScalar h;
70: DMDAGetInfo(dmmg->dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
71: h = 1.0/((mx-1)*(my-1)*(mz-1));
72: VecSet(b,h);
73: return(0);
74: }
75:
78: PetscErrorCode ComputeMatrix(DMMG dmmg,Mat jac,Mat B)
79: {
80: DM da = dmmg->dm;
82: PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
83: PetscScalar v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
84: MatStencil row,col[7];
86: DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
87: Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
88: HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
89: DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
90:
91: for (k=zs; k<zs+zm; k++){
92: for (j=ys; j<ys+ym; j++){
93: for(i=xs; i<xs+xm; i++){
94: row.i = i; row.j = j; row.k = k;
95: if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
96: v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
97: MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
98: } else {
99: v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
100: v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
101: v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
102: v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
103: v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
104: v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
105: v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
106: MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
107: }
108: }
109: }
110: }
111: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
112: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
113: return 0;
114: }