/*$Id: ex22.c,v 1.9 2000/09/28 14:46:50 bsmith Exp $*/ /* Laplacian in 3D. Modeled by the partial differential equation Laplacian u = 0,0 < x,y,z < 1, with boundary conditions u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1. This uses multigrid to solve the linear system See ex18.c for a simpler example that does not use multigrid */ static char help[] = "Solves 3D Laplacian using multigrid.\n\ The command line options are:\n\ -mx <xg>, where <xg> = number of grid points in the x-direction\n\ -my <yg>, where <yg> = number of grid points in the y-direction\n\ -mz <zg>, where <zg> = number of grid points in the z-direction\n\n"; #include "petscda.h" #include "petscsles.h" #include "petscmg.h" extern int ComputeJacobian(DAMG,Mat); extern int ComputeRHS(DAMG,Vec); #undef __FUNC__ #define __FUNC__ "main" int main(int argc,char **argv) { int ierr,i,sw = 1,dof = 1,mx = 2,my = 2,mz = 2,nlevels = 3; DAMG *damg; SLES sles; Scalar one = 1.0, mone = -1.0; PetscReal norm; PetscInitialize(&argc,&argv,(char *)0,help); ierr = OptionsGetInt(0,"-stencil_width",&sw,0);CHKERRQ(ierr); ierr = OptionsGetInt(0,"-dof",&dof,0);CHKERRQ(ierr); ierr = OptionsGetInt(PETSC_NULL,"-mx",&mx,PETSC_NULL);CHKERRA(ierr); ierr = OptionsGetInt(PETSC_NULL,"-my",&my,PETSC_NULL);CHKERRA(ierr); ierr = OptionsGetInt(PETSC_NULL,"-mz",&mz,PETSC_NULL);CHKERRA(ierr); ierr = DAMGCreate(PETSC_COMM_WORLD,nlevels,PETSC_NULL,&damg);CHKERRQ(ierr); ierr = DAMGSetGrid(damg,3,DA_NONPERIODIC,DA_STENCIL_STAR,mx,my,mz,sw,dof);CHKERRQ(ierr); ierr = DAMGSetSLES(damg,ComputeRHS,ComputeJacobian);CHKERRQ(ierr); ierr = DAMGSolve(damg);CHKERRQ(ierr); ierr = MatMult(DAMGGetJ(damg),DAMGGetx(damg),DAMGGetr(damg));CHKERRQ(ierr); ierr = VecAXPY(&mone,DAMGGetb(damg),DAMGGetr(damg));CHKERRQ(ierr); ierr = VecNorm(DAMGGetr(damg),NORM_2,&norm);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Residual norm %g\n",norm);CHKERRQ(ierr); ierr = DAMGDestroy(damg);CHKERRQ(ierr); PetscFinalize(); return 0; } #undef __FUNC__ #define __FUNC__ "ComputeRHS" int ComputeRHS(DAMG damg,Vec b) { int ierr,mx,my,mz; Scalar h; PetscFunctionBegin; ierr = DAGetInfo(damg->da,0,&mx,&my,&mz,0,0,0,0,0,0,0);CHKERRQ(ierr); h = 1.0/((mx-1)*(my-1)*(mz-1)); ierr = VecSet(&h,b);CHKERRQ(ierr); PetscFunctionReturn(0); } #undef __FUNC__ #define __FUNC__ "ComputeJacobian" int ComputeJacobian(DAMG damg,Mat jac) { DA da = damg->da; int *ltog,ierr,i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,Xm,Ym,Zm,Xs,Ys,Zs,row,nloc,col[7],base1,grow; Scalar two = 2.0,one = 1.0,v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy; ierr = DAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0);CHKERRQ(ierr); Hx = one / (double)(mx-1); Hy = one / (double)(my-1); Hz = one / (double)(mz-1); HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx; ierr = DAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr); ierr = DAGetGhostCorners(da,&Xs,&Ys,&Zs,&Xm,&Ym,&Zm);CHKERRQ(ierr); ierr = DAGetGlobalIndices(da,&nloc,<og);CHKERRQ(ierr); for (k=zs; k<zs+zm; k++){ base1 = (k-Zs)*(Xm*Ym); for (j=ys; j<ys+ym; j++){ row = base1 + (j-Ys)*Xm + xs - Xs - 1; for(i=xs; i<xs+xm; i++){ row++; grow = ltog[row]; if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1){ ierr = MatSetValues(jac,1,&grow,1,&grow,&one,INSERT_VALUES); CHKERRQ(ierr); continue; } v[0] = -HxHydHz; col[0] = ltog[row - Xm*Ym]; v[1] = -HxHzdHy; col[1] = ltog[row - Xm]; v[2] = -HyHzdHx; col[2] = ltog[row - 1]; v[3] = two*(HxHydHz + HxHzdHy + HyHzdHx); col[3]=grow; v[4] = -HyHzdHx; col[4] = ltog[row + 1]; v[5] = -HxHzdHy; col[5] = ltog[row + Xm]; v[6] = -HxHydHz; col[6] = ltog[row + Xm*Ym]; ierr = MatSetValues(jac,1,&grow,7,col,v,INSERT_VALUES);CHKERRQ(ierr); } } } ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); return 0; }