On Thu, Feb 16, 2012 at 12:54 PM, <[email protected]> wrote:

Dear list,

I would like to parallelize a multigrid code by Petsc. I do not want to use the DMMG infrastructure, since it will be replaced in the next PETSc release. Therefore I preferred to use the multigrid as a preconditioner. In practice, I use the Richardson iteration, choosing the same matrix of the linear system as a preconditioner, so that I think the Richardson iteration should converge in only one iteration, and effectively it is like solving the whole linear system by the multigrid.

Your understanding of the Richardson iteration is flawed. You can consult Yousef Saad's book for the standard definition and anaysis.

As a first test, I tried to use a one-grid multigrid (then not a truly multigrid). I just set the coarse solver (by a standard KSPSolve), and it should be enough, because the multigrid starts already from the coarsest grid and then it does not need the smoother and the transfer operators. Unfortunately, the iteration scheme (which should be the Richardson scheme) converges with a reason=4 (KSP_CONVERGED_ITS) to a wrong solution. On the other hand, if I solve the whole problem with the standard KSPSolve (then withouth setting the multigrid as a preconditioner ...), it converges to the right solution with a reason=2.

Yes, give Richardson many more iterations, -ksp_max_it. Matt

I thought that the two methods should be the exactly the same method, and I do not understand why they provide different convergence results.

Here is the relevant code:

// Set the matrix of the linear system Mat Mcc; ierr=MatCreate(PETSC_COMM_**WORLD,&Mcc); CHKERRQ(ierr); ierr=MatSetType(Mcc, MATMPIAIJ); CHKERRQ(ierr); ierr=MatSetSizes(Mcc,PETSC_**DECIDE,PETSC_DECIDE,1000,1000)**; CHKERRQ(ierr); ierr=setMatrix(Mcc); //It is a routine that set the values of the matrix Mcc

// Set the ksp solver with the multigrid as a preconditioner KSP ksp, KspSolver; ierr = KSPCreate(PETSC_COMM_WORLD,&**ksp);CHKERRQ(ierr); ierr = KSPSetType(ksp,KSPRICHARDSON); ierr = KSPGetPC(ksp,&pc);CHKERRQ(**ierr); ierr = PCSetType(pc,PCMG);CHKERRQ(**ierr); ierr = PCMGSetLevels(pc,1,&PETSC_**COMM_WORLD);CHKERRQ(ierr); ierr = PCMGSetType(pc,PC_MG_**MULTIPLICATIVE);CHKERRQ(ierr); ierr = PCMGGetCoarseSolve(pc,&**kspCoarseSolve);CHKERRQ(ierr); ierr = KSPSetOperators(**kspCoarseSolve,Mcc,Mcc,** DIFFERENT_NONZERO_PATTERN);**CHKERRQ(ierr); ierr = KSPSetTolerances(**kspCoarseSolve,1.e-12,PETSC_** DEFAULT,PETSC_DEFAULT,PETSC_**DEFAULT);CHKERRQ(ierr); ierr = KSPSetOperators(ksp,Mcc,Mcc,**DIFFERENT_NONZERO_PATTERN);** CHKERRQ(ierr); ierr = KSPSetTolerances(ksp,1.e-12,**PETSC_DEFAULT,PETSC_DEFAULT,** PETSC_DEFAULT);CHKERRQ(ierr); ierr = KSPSolve(ksp,RHS,U);CHKERRQ(**ierr);

// Solve with the standard KSPSolve KSP ksp1; ierr = KSPCreate(PETSC_COMM_WORLD,&**ksp1);CHKERRQ(ierr); ierr = KSPSetOperators(ksp1,Mcc,Mcc,**DIFFERENT_NONZERO_PATTERN);** CHKERRQ(ierr); ierr = KSPSetTolerances(ksp1,1.e-12/(**2*nn123),PETSC_DEFAULT,PETSC_** DEFAULT,PETSC_DEFAULT);**CHKERRQ(ierr); ierr = KSPSolve(ksp1,RHS,U1);CHKERRQ(**ierr);

At the end, the Vector U and U1 are different. Thank you.

Best regards, Armando

-- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener