[petsc-users] Preconditioners for a FEM model

[murat keçeli]

Hi Jifeng,

You can start with ex13 in SLEPc to see how it works for your case. You
would need MUMPS as a direct solver. Section 3.4.5 is the relevant section
in SLEPc manual (Campos and Roman 2012 paper would be very helpful if you
need more details). Let me know if it works for you and we can continue
from there.

Thanks,
Murat


On Thu, Jul 3, 2014 at 12:18 AM, jifeng zhao <
jifengzhao2015 at u.northwestern.edu> wrote:

> Hi Murat,
>
> Yes, that sounds great. I would like to have a try. Would you let me know
> how to use it on top of SLEPC and PETSC in more details?
>
> Cheers,
> Jifeng Zhao
>
>
> On Wed, Jul 2, 2014 at 9:41 PM, murat keçeli <keceli at gmail.com> wrote:
>
>> Hi Jifeng,
>>
>> I think your application is suitable for the SIPs method, see attached
>> paper.  We have improved it recently, so that it can handle very
>> large (500k by 500k with more than 3.e7 nonzeros) sparse matrices.Current
>> version of SIPs is basically adding a second layer of parallelism on top of
>> SLEPc's shift and invert method. Let me or Hong Zhang (cc, the developer of
>> SIPs) know, if you would like to give it a try.
>>
>> Murat Keceli
>>
>>
>> On Wed, Jul 2, 2014 at 4:46 PM, jifeng zhao <
>> jifengzhao2015 at u.northwestern.edu> wrote:
>>
>>> Hello all,
>>>
>>> I am working on solving a generalized eigenvalue problem with SLEPC and
>>> PETSC.
>>>
>>> *K* x = lamda *M* x
>>>
>>> I attached the sparsity pattern of matrix *M* (*K* is the same). It is
>>> a FEM model. It is so sparse is because of constraints.
>>>
>>> I have tried two things:
>>>
>>> 1. Krylov-Schur and exact shift-and-invert (I will try MUMPS in
>>> future). It works. But I am worrying that it is less parrallelable, when
>>> the problem contains millions of degree of freedom.
>>>
>>> 2. JD with Jacobi preconditioner. It could work, but a lot of tuning
>>> needs to be done in terms of RTOL, max_iteration_number. And sometimes I
>>> suffer from a stagnated solution, and can't obtain accurate result.
>>>
>>> Does anybody know that for my specific case of matrix sparsity, is there
>>> any thing I can do to speed up my direct solver (Krylov-Schur)?
>>>
>>> Is there any recommended preconditioners I could try on, for the case of
>>> JD? There are a lot of preconditioners in HYPRE library.
>>>
>>> Thank you in advance!
>>> [image: Inline image 1]
>>>  --
>>> Jifeng Zhao
>>> PhD candidate at Northwestern University, US
>>> Theoretical and Applied Mechanics Program
>>>
>>
>>
>
>
> --
> Jifeng Zhao
> PhD candidate at Northwestern University, US
> Theoretical and Applied Mechanics Program
>
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