Actual source code: ex22.c

  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: int main(int argc,char **argv)
 25: {
 26:   int         ierr;
 27:   DMMG        *dmmg;
 28:   PetscScalar mone = -1.0;
 29:   PetscReal   norm;
 30:   DA          da;

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

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

 39:   DMMGSetSLES(dmmg,ComputeRHS,ComputeJacobian);

 41:   DMMGSolve(dmmg);

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

 48:   DMMGDestroy(dmmg);
 49:   PetscFinalize();

 51:   return 0;
 52: }

 54: int ComputeRHS(DMMG dmmg,Vec b)
 55: {
 56:   int    ierr,mx,my,mz;
 57:   PetscScalar h;

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

 73:   DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);
 74:   Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
 75:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
 76:   DAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);
 77: 
 78:   for (k=zs; k<zs+zm; k++){
 79:     for (j=ys; j<ys+ym; j++){
 80:       for(i=xs; i<xs+xm; i++){
 81:         row.i = i; row.j = j; row.k = k;
 82:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){
 83:           v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
 84:           MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);
 85:         } else {
 86:           v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
 87:           v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
 88:           v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
 89:           v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
 90:           v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
 91:           v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
 92:           v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
 93:           MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);
 94:         }
 95:       }
 96:     }
 97:   }
 98:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
 99:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
100:   return 0;
101: }