2: /*$Id: ex22.c,v 1.19 2001/08/07 21:30:54 bsmith Exp $*/
  3: /*
  4: Laplacian in 3D. Modeled by the partial differential equation

  6:    Laplacian u = 1,0 < x,y,z < 1,

  8: with boundary conditions

 10:    u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.

 12:    This uses multigrid to solve the linear system

 14: */

 16: static char help[] = "Solves 3D Laplacian using multigrid.nn";

 18:  #include petscda.h
 19:  #include petscsles.h

 21: extern int ComputeJacobian(DMMG,Mat);
 22: extern int ComputeRHS(DMMG,Vec);

 24: #undef __FUNCT__
 26: int main(int argc,char **argv)
 27: {
 28:   int         ierr;
 29:   DMMG        *dmmg;
 30:   PetscScalar mone = -1.0;
 31:   PetscReal   norm;
 32:   DA          da;

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

 36:   DMMGCreate(PETSC_COMM_WORLD,3,PETSC_NULL,&dmmg);
 37:   DACreate3d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,3,3,3,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,0,&da);
 38:   DMMGSetDM(dmmg,(DM)da);
 39:   DADestroy(da);

 41:   DMMGSetSLES(dmmg,ComputeRHS,ComputeJacobian);

 43:   DMMGSolve(dmmg);

 45:   MatMult(DMMGGetJ(dmmg),DMMGGetx(dmmg),DMMGGetr(dmmg));
 46:   VecAXPY(&mone,DMMGGetb(dmmg),DMMGGetr(dmmg));
 47:   VecNorm(DMMGGetr(dmmg),NORM_2,&norm);
 48:   /* PetscPrintf(PETSC_COMM_WORLD,"Residual norm %gn",norm); */

 50:   DMMGDestroy(dmmg);
 51:   PetscFinalize();

 53:   return 0;
 54: }

 56: #undef __FUNCT__
 58: int ComputeRHS(DMMG dmmg,Vec b)
 59: {
 60:   int    ierr,mx,my,mz;
 61:   PetscScalar h;

 64:   DAGetInfo((DA)dmmg->dm,0,&mx,&my,&mz,0,0,0,0,0,0,0);
 65:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
 66:   VecSet(&h,b);
 67:   return(0);
 68: }
 69: 
 70: #undef __FUNCT__
 72: int ComputeJacobian(DMMG dmmg,Mat jac)
 73: {
 74:   DA           da = (DA)dmmg->dm;
 75:   int          ierr,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
 76:   PetscScalar  v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
 77:   MatStencil   row,col[7];

 79:   DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);
 80:   Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
 81:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
 82:   DAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
 83: 
 84:   for (k=zs; k<zs+zm; k++){
 85:     for (j=ys; j<ys+ym; j++){
 86:       for(i=xs; i<xs+xm; i++){
 87:         row.i = i; row.j = j; row.k = k;
 88:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
 89:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
 90:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
 91:         } else {
 92:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
 93:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
 94:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
 95:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
 96:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
 97:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
 98:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
 99:           MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
100:         }
101:       }
102:     }
103:   }
104:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
105:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
106:   return 0;
107: }