[petsc-users] Richardson with multiplicative MG vs. full MG

[Jed Brown]

Thanks.

http://petsc.cs.iit.edu/petsc/petsc-dev/rev/194943551e3d

On Mon, Aug 13, 2012 at 2:41 PM, John Fettig <john.fettig at gmail.com> wrote:

> It appears the documentation for PCMG has this spelled wrong:
>
> -pc_mg_type <additive,multiplicative,full,cascade> - multiplicative is
> the default
>
> John
>
> On Mon, Aug 13, 2012 at 4:19 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
> > Shorthand for this is -pc_mg_type kaskade.
> >
> >
> > On Mon, Aug 13, 2012 at 1:01 PM, John Fettig <john.fettig at gmail.com>
> wrote:
> >>
> >> Barry,
> >>
> >> Thank you for answering my question.  I have another one for you:  it
> >> seems the special case of zero pre-smooths is somewhat non-trivial.
> >> The best I can do is set the pre-smoother to Richardson with PCNONE
> >> and zero as max_its. However, if you aren't careful in setting
> >> KSPSetInitialGuessNonzero this can have unexpected results since the
> >> generic KSPSolve will clobber your solution before it even tries a
> >> convergence criteria (thus ruling out KSPPREONLY).  It also does a
> >> couple of unnecessary residual calculations. Would it be reasonable to
> >> put a zero-iteration special case in KSPSolve so that if you don't
> >> want any iterations it doesn't actually do anything (no setup, no
> >> preconditioner, no residual, no scaling, etc.)?
> >>
> >> Thanks,
> >> John
> >>
> >> On Thu, Aug 9, 2012 at 6:37 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >> >
> >> >   John,
> >> >
> >> > On Aug 9, 2012, at 9:50 AM, John Fettig <john.fettig at gmail.com>
> wrote:
> >> >
> >> >> I am a little confused about what Richardson means.  If you use
> >> >> multiplicative V-cycle multigrid with Richardson KSP (and no
> >> >> convergence monitor), it sets the applyrichardson operator to
> >> >> PCApplyRichardson_MG, which appears to just run V-cycles until
> >> >> convergence.
> >> >
> >> >      Yes, this is correct.
> >> >
> >> >>  As far as I can tell, it doesn't ever update according
> >> >> to the documented
> >> >>
> >> >> x^{n+1} = x^{n} + scale*B(b - A x^{n})
> >> >>
> >> >       In exact arithmetic it is actually "implicitly" doing exactly
> this
> >> > update.  It is difficult to see why this is true generally (because B
> is
> >> > rather complicated for multigrid) but if you consider only two levels
> with a
> >> > direct solver on the coarse grid and SSOR as the pre and post smooth
> you can
> >> > write out the formulas and map back and forth between the two forms.
>  The
> >> > reason for the PCApplyRichardson_ forms is because they are a bit more
> >> > efficient than  separating out the action of B and then doing the
> update as
> >> > above.
> >> >
> >> >
> >> >> If on the other hand you use full MG, it does update according to the
> >> >> above formula.  This also happens if you set a convergence monitor.
> >> >>
> >> >> I can see how multiplicative V-cycle with Richardson is simply using
> >> >> multigrid as a solver.  What I don't understand is how full MG with
> >> >> Richardson is using multigrid as a solver, because it is using the
> >> >> update formula above in between cycles..  Shouldn't there be a
> >> >> applyrichardson for full multigrid as well?  If not, why?
> >> >
> >> >     I think there could be a applyRichardson for full multigrid but it
> >> > would be kind of complicated and would not benefit much because the
> amount
> >> > of work in a full multigrid step is much higher so the savings would
> be a
> >> > much lower percentage than with V cycle.
> >> >
> >> >    Barry
> >> >
> >> >>
> >> >> Thanks,
> >> >> John
> >> >
> >
> >
>
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