[petsc-users] Convergence criterion for composite preconditioner

[Barry Smith]

On Apr 30, 2014, at 2:01 PM, Federico Marini <federico.marini at unimi.it> wrote:

>  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.

   Be careful here. By default PCASM uses RASM (restricted Additive Schwarz method) which is not a symmetric preconditioner so will not work properly with KSPCG.  You can use PCASMSetType(pc1, PC_ASM_BASIC) or -sub_1_pc_asm_type basic 


> 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.

   The default test for CG uses left preconditioner and the relative decrease in the preconditioned residual norm. So in this case it is 2.938575711894e-06/initialpreconditionednorm and 4.409443889428e-05/initialpreconditionednorm. Since you didn’t send the 0th iteration I don’t know what the initial norms are but I am confident it has decreased by 1e-7. 

   BTW: with CG you can use -ksp_norm_type preconditioned or unpreconditioned or natural   or KSPSetNormType(ksp, see the manual page) to use different norms for testing.

  Barry

> 
> Can anyone explain me why?
> 
> Thank you in advance,
> Federico Marini
> 
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