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?
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
