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: }