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: }