Actual source code: ex45.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:    The same as ex22.c except it does not use DMMG, it uses its replacement.
 14:    See src/snes/examples/tutorials/ex50.c

 16:    Can also be run with -pc_type exotic -ksp_type fgmres

 18: */

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

 22: #include <petscksp.h>
 23: #include <petscdmda.h>


 31: int main(int argc,char **argv)
 32: {
 34:   KSP            ksp;
 35:   PetscReal      norm;
 36:   DM             da;
 37:   Vec            x,b,r;
 38:   Mat            A;

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

 42:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 43:   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);
 44:   DMSetInitialGuess(da,ComputeInitialGuess);
 45:   DMSetFunction(da,ComputeRHS);
 46:   DMSetJacobian(da,ComputeMatrix);
 47:   KSPSetDM(ksp,da);
 48:   /*  KSPSetDMActive(ksp,PETSC_FALSE);*/
 49:   DMDestroy(&da);

 51:   KSPSetFromOptions(ksp);
 52:   KSPSetUp(ksp);
 53:   KSPSolve(ksp,PETSC_NULL,PETSC_NULL);
 54:   KSPGetSolution(ksp,&x);
 55:   KSPGetRhs(ksp,&b);
 56:   VecDuplicate(b,&r);
 57:   KSPGetOperators(ksp,&A,PETSC_NULL,PETSC_NULL);

 59:   MatMult(A,x,r);
 60:   VecAXPY(r,-1.0,b);
 61:   VecNorm(r,NORM_2,&norm);
 62:   PetscPrintf(PETSC_COMM_WORLD,"Residual norm %G\n",norm);

 64:   VecDestroy(&r);
 65:   KSPDestroy(&ksp);
 66:   PetscFinalize();

 68:   return 0;
 69: }

 73: PetscErrorCode ComputeRHS(DM dm,Vec x,Vec b)
 74: {
 76:   PetscInt       mx,my,mz;
 77:   PetscScalar    h;
 78:   PetscScalar    ***xx,***bb;
 79:   PetscInt       i,j,k,xm,ym,zm,xs,ys,zs;
 80:   PetscScalar    Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;

 83:   DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
 84:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
 85:   VecSet(b,h);

 87:   if (x) {
 88:     DMDAVecGetArray(dm,x,&xx);
 89:     DMDAVecGetArray(dm,b,&bb);

 91:   DMDAGetInfo(dm,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
 92:   Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
 93:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
 94:   DMDAGetCorners(dm,&xs,&ys,&zs,&xm,&ym,&zm);
 95: 
 96:   for (k=zs; k<zs+zm; k++){
 97:     for (j=ys; j<ys+ym; j++){
 98:       for(i=xs; i<xs+xm; i++){
 99:         if (!(i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1)){
100:           bb[k][j][i] -= +HxHydHz*xx[k-1][j][i] + HxHzdHy*xx[k][j-1][i] + HyHzdHx*xx[k][j][i-1] + HyHzdHx*xx[k][j][i+1] + HxHzdHy*xx[k][j+1][i] + HxHydHz*xx[k+1][j][i];
101:         }
102:         bb[k][j][i] += 2.0*(HxHydHz + HxHzdHy + HyHzdHx)*xx[k][j][i];
103:       }
104:     }
105:   }
106:     DMDAVecRestoreArray(dm,x,&xx);
107:     DMDAVecRestoreArray(dm,b,&bb);
108:   }
109:   return(0);
110: }
111: 
114: PetscErrorCode ComputeInitialGuess(DM dm,Vec b)
115: {

119:   VecSet(b,0);
120:   return(0);
121: }

125: PetscErrorCode ComputeMatrix(DM dm,Vec x,Mat jac,Mat B,MatStructure *stflg)
126: {
127:   DM             da = dm;
129:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
130:   PetscScalar    v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
131:   MatStencil     row,col[7];

133:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
134:   Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
135:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
136:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
137: 
138:   for (k=zs; k<zs+zm; k++){
139:     for (j=ys; j<ys+ym; j++){
140:       for(i=xs; i<xs+xm; i++){
141:         row.i = i; row.j = j; row.k = k;
142:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
143:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
144:           MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);
145:         } else {
146:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
147:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
148:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
149:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
150:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
151:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
152:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
153:           MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);
154:         }
155:       }
156:     }
157:   }
158:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
159:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
160:   *stflg = SAME_NONZERO_PATTERN;
161:   return 0;
162: }