[petsc-users] matrix-free methods

[Matthew Knepley]

On Mon, May 7, 2012 at 2:15 PM, <coco at dmi.unict.it> wrote:

> Dear all,
>
> I am trying to use a matrix-free method to solve a linear system with
> Petsc. In particular, I noticed that if I solve the same linear system with
> the same KSP solver, the same preconditioner, and the same options, I
> obtain different convergence results if I solve the system with the full-
> or free-matrix method. Is that plausible?
>

Always always always use -ksp_view to see what you are actually doing. The
default for actual matrices is ILU(0), since we can
calculate it. The default for Shell matrices is nothing, since we have no
matrix to calculate from. Thus, the inferior convergence.

   Matt


> Here is a piece of code:
>
> //Method #1:
> ierr=MatCreate(PETSC_COMM_**WORLD,&M); CHKERRQ(ierr);
> ierr=MatSetType(M, MATMPIAIJ); CHKERRQ(ierr);
> ierr=MatSetSizes(M,PETSC_**DECIDE,PETSC_DECIDE,N,M); CHKERRQ(ierr);
> [...filling the matrix...]
> ierr = KSPCreate(PETSC_COMM_WORLD,&**ksp);CHKERRQ(ierr);
> ierr = KSPSetOperators(ksp,M,M,**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);
>
> //Method #2:
> extern PetscErrorCode UserMult(Mat,Vec,Vec);
> ierr=MatCreateShell(PETSC_**COMM_WORLD,N,M,n,M,ctx,&M1); CHKERRQ(ierr);
> ierr=MatShellSetOperation(M,**MATOP_MULT,(void(*)(void)) UserMult);
> CHKERRQ(ierr);
> ierr=MatAssemblyBegin(M,MAT_**FINAL_ASSEMBLY); CHKERRQ(ierr);
> ierr=MatAssemblyEnd(M,MAT_**FINAL_ASSEMBLY); CHKERRQ(ierr);
> ierr = KSPCreate(PETSC_COMM_WORLD,&**ksp1);CHKERRQ(ierr);
> ierr = KSPSetOperators(ksp1,M1,M1,**DIFFERENT_NONZERO_PATTERN);**
> CHKERRQ(ierr);
> ierr = KSPSetTolerances(ksp1,1.e-12,**PETSC_DEFAULT,PETSC_DEFAULT,**
> PETSC_DEFAULT);CHKERRQ(ierr);
> ierr = KSPSolve(ksp1,RHS,U1);CHKERRQ(**ierr);
>
> In particular, the method #1 converges in 15 iterations, while the method
> #2 in more than 1000.
>
> Thank you in advance.
> 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
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