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

[Dave Lee]

Thanks for the tip Jed,

I will look into this. I'm currently trying to figure out if there's any
way I can get away with using the existing L2 norm, and if not GCR sounds
like a good alternative to pursue.

Cheers, Dave.

On Fri, Jul 5, 2019 at 11:02 PM Jed Brown <jed at jedbrown.org> wrote:

> Dave, have you considered using GCR instead of FGMRES?  It's a flexible
> method that is equivalent in many circumstances, but provides the
> residual and solution at each iteration without needing to "build" it.
>
> Dave Lee via petsc-users <petsc-users at mcs.anl.gov> writes:
>
> > 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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