[petsc-users] Convergence criterion for composite preconditioner

[Federico Marini]

 Dear PETSc users,

I implemented PCCOMPOSITE preconditioner of type PC_COMPOSITE_ADDITIVE. It has two components:

 - pc1: PCASM 1-level additive Schwarz preconditioning
 - pc2: PCSHELL 2-level additive Schwarz preconditioning

so basically the whole preconditioner is a 2-level additive Schwarz preconditioner, where the second level is hand-made in a MATSHELL matrix structure. For PCASM, I use defalut options. I run tests with PCSHELL activated and deactivated.

I use the default stopping criterion with this setting:

ierr=KSPSetTolerances(ksp,1e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);

In the end I get these convergence results with 256 MPI tasks (1054729 total dofs) using KSPCG

 PSASM only:
 ...
134 KSP preconditioned resid norm 4.680038240771e-06 true resid norm 5.417972183036e-07 ||r(i)||/||b|| 2.402197263846e-06
135 KSP preconditioned resid norm 3.681603361690e-06 true resid norm 4.091445069661e-07 ||r(i)||/||b|| 1.814047363013e-06
136 KSP preconditioned resid norm 2.938575711894e-06 true resid norm 3.280865690135e-07 ||r(i)||/||b|| 1.454656155040e-06
 - convergence detected

 PCASM + PCSHELL
 ...
 22 KSP preconditioned resid norm 6.610753500258e-05 true resid norm 4.725684013113e-06 ||r(i)||/||b|| 2.095253504927e-05
 23 KSP preconditioned resid norm 1.173818907551e-04 true resid norm 2.984650385207e-06 ||r(i)||/||b|| 1.323321483881e-05
 24 KSP preconditioned resid norm 4.409443889428e-05 true resid norm 1.959757043931e-06 ||r(i)||/||b|| 8.689086709369e-06
 - convergence detected

The preconditioner, in both (1- and 2-level) versions, works fine, but the relative residual norm stopping criterion is not achieved. Observing the residual norms, I don't think the next iteration would achieve the requested 10^-7 tolerance.

Can anyone explain me why?

Thank you in advance,
Federico Marini

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