[petsc-users] V-cycle multigrid with matrix shells

[Sylvain Barbot]

Dear Jed,

During my recent visit to ETH, I talked at length about multi-grid
with Dave May who warned me about the issues of large
coefficient-contrasts. Most of my problems of interest for
tectonophysics and earthquake simulations are cases of relatively
smooth variations in elastic moduli. So I am not too worried about
this aspect of the problem. I appreciate your advice about trying
simpler solutions first. I have tested at length direct solvers of 2-D
and 3-D problems of elastic deformation and I am quite happy with the
results. My primary concern now is computation speed, especially for
3-D problems, where i have of the order 512^3 degrees of freedom. I
was planning to test Jacobi and SOR smoothers. Is there another
smoother you recommend for this kind of problem?

Thanks,
Sylvain

2011/5/11 Jed Brown <jed at 59a2.org>:
> On Wed, May 11, 2011 at 04:20, Sylvain Barbot <sylbar.vainbot at gmail.com>
> wrote:
>>
>> I am still trying to design a
>> multigrid preconditionner for the Navier's equation of elasticity.
>
> I have heard, through an external source, that you have large jumps in both
> Young's modulus and Poisson ratio that are not grid aligned, including
> perhaps thin structures that span a large part of the domain. Such problems
> are pretty hard, so I suggest you focus on robustness and do not worry about
> low-memory implementation at this point. That is, you should assemble the
> matrices in a usual PETSc format instead of using MatShell to do everything
> matrix-free. This gives you access to much stronger smoothers.
> After you find a scheme that is robust enough for your purposes, _then_ you
> can make it low-memory by replacing some assembled matrices by MatShell. To
> realize most of the possible memory savings, it should be sufficient to do
> this on the finest level only.