[petsc-users] Computing residual norm in KSPFGMRESCycle()

[Dave Lee]

Hi Matt and Barry,

thanks for the good ideas.

I wasn't aware of the function KSPSetConvergenceTest(), thanks for alerting
me to this Matt. Unfortunately I really do need to exclude a couple of
specific degrees of freedom from the norm, and as such I want to make sure
I can replicate the norm as computed within UpdateHessenberg() before I
replace this.

Apologies Barry, there was a stupid bug in that code, it should have read:
    KSPFGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm);
    KSPFGMRESBuildSoln(fgmres->nrs,ksp->vec_sol,tmp_sol,ksp,loc_it+1);
    VecAXPY(tmp_sol,-1.0,ksp->vec_rhs);
    VecNorm(tmp_sol,NORM_2,&res_tmp);

Which does not give the same result as the norm for UpdateHessenberg().
Unfortunately I want to avoid using
KSPBuildResidual(ksp,NULL,NULL,&resid);
as this calls KSP_MatMult(), which will in turn call my snes residual
assembly routine. This routine in turn calls a Navier Stokes solver to run
for a fixed (long) time period, and so is expensive.

Replacing VecNorm() with my own version is indeed what I'm doing elsewhere,
I'm just not sure of how to replace the UpdateHessenberg() norm right now.

Cheers, Dave.

On Fri, Jul 5, 2019 at 12:59 PM Smith, Barry F. <bsmith at mcs.anl.gov> wrote:

>
>
> > On Jul 4, 2019, at 7:29 PM, Dave Lee via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
> >
> > Hi PETSc,
> >
> > I have a problem for which I need to exclude certain degrees of freedom
> from the evaluation of the norm as used to monitor the residual in FGMRES
> (don't ask!). Therefore I would like to replace the existing norm
> evaluation with my own version.
> >
> > Currently this is done within:
> > KSPFGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm)
> > as:
> > *res = PetscAbsScalar(*RS(it+1));
> >
> > Firstly, I would like to make sure I can replicate the existing residual
> norm. I tried to do this as:
> > KSPFGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm);
> > KSPFGMRESBuildSoln(fgmres->nrs,ksp >vec_sol,tmp_sol,ksp,loc_it);
>
>    I don't understand the lines of code below. I don't see how they could
> compute the norm of the residual.
>
> From KSPMonitorTrueResidualNorm() you can compute the unpreconditioned
> residual with
>
>   ierr = KSPBuildResidual(ksp,NULL,NULL,&resid);CHKERRQ(ierr);
>   ierr = VecNorm(resid,NORM_2,&truenorm);CHKERRQ(ierr);
>   ierr = VecDestroy(&resid);CHKERRQ(ierr);
>
> since FGMRES always uses right preconditioning (and hence the
> unpreconditioned residual) this should match the value computed internally
> by FGMRES (subject to roundoff differences)
>
> To exclude certain values in the residual from the norm calculation you
> could write a custom "VecNorm" norm that skipped those entries.
>
>   Barry
>
>
>
>
>
> > VecNorm(tmp_sol,NORM_2,&res_tmp);
> > VecNorm(ksp->vec_rhs,NORM_2,&res_rhs);
> > res_norm = fabs(res_tmp-res_rhs);
> >
> > But this doesn't match the norm that comes out of UpdateHessenberg.
> >
> > Any ideas on how I can re-create the norm derived from UpdateHessenberg
> as an expansion over the Kyrlov vectors in FGMRES?
> >
> > Cheers, Dave.
>
>
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