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

[Matthew Knepley]

On Thu, May 12, 2011 at 9:51 AM, Sanjay Govindjee <s_g at berkeley.edu> wrote:

> Sylvain,
>
> Is there a reason you are not using Prometheus (--download_prometheus=1)
> for your MG preconditioner?
> It was designed with 3D solid mechanics in mind.



I would also point out that even for power law problems, PyLith uses ML and
PCFIELDSPLIT for the elastic
solver and it works great. Have you tried this?

  Thanks,

     Matt


>
> -sanjay
>
>
>
> On 5/11/11 11:12 PM, Sylvain Barbot wrote:
>
>> 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.
>>>
>>


-- 
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
-- Norbert Wiener
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