[petsc-users] matrix-free methods

[Jed Brown]

On Mon, May 7, 2012 at 12:15 PM, <coco at dmi.unict.it> wrote:

> 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?
>
> 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.
>

What preconditioner?

How did you determine that the matrix-free method applies the same linear
operator?
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