[petsc-users] boomerAmg scalability

[Mohamad M. Nasr-Azadani]

Thank you Jed for the detailed explanation. To tell you the truth, that was
a bit overwhelming/scary for an engineer like me-that I have to be
supercareful when using those solvers and preconditioners- :D
For my case though, I decided to fix the pressure at one node in the domain
so  I won't end up with a null-space case of the Pressure equation. I
assume that way, I would not have to worry about the nullspace problems and
the convergence issues you pointed out, right?

Best,
Mohamad



On Mon, Dec 19, 2011 at 9:09 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Mon, Dec 19, 2011 at 20:57, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>> So please tell use how we SHOULD use AMG with those "indefinite problem
>> produced by most discretizations of incompressible flow" dear teacher :-)
>
>
> If only there was a nice complete answer...
>
> We can do block preconditioners advocated by Elman and others. These are
> the most flexible and the simplest for code reuse. For low Reynolds number,
> they can also have optimal complexity, although the constants are usually
> not the best. Most variants are well-supported by PCFieldSplit (e.g. with
> PCLSC), but some need the user to provide auxiliary operators (e.g. the
> "pressure convection-diffusion" variant). We could improve support for
> these cases, but it's a delicate balance and I don't know any way to avoid
> asking the user to understand a reasonable amount about the method and
> usually to provide auxiliary information.
>
> We can do coupled multigrid with fieldsplit or "distributed relaxation" as
> a smoother. These can often be made more robust, but they tend to be more
> intrusive to implement. These are not usually purely algebraic due to
> inf-sup issues when coarsening the dual variables (pressure), though Mark
> Adams' work on this for contact mechanics could be used to coarsen pressure
> algebraically. I would like to experiment with this in PCGAMG.
>
> We can do coupled multigrid with compatible Vanka-type smoothers. Whether
> these are algorithmically effective and/or efficient is quite dependent on
> the discretization. These methods are also usually geometric, though it's
> possible to algebraically define a Vanka-smoother (though not necessarily
> efficient). This is straightforward for MAC finite differences on
> structured grids. For continuous finite elements, the "rotated Q1"
> Rannacher-Turek elements are most attractive for these smoothers, but
> Rannacher-Turek elements do not satisfy a discrete Korn's inequality, so
> they are unusable for many problems. Some variants of DG for incompressible
> flow seem to be the most interesting for this approach in general domains.
>
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