[petsc-users] Preconditioners for a FEM model

[Hong Zhang]

venkatesh:

>
>  Is it possible to do a non-symmetric complex eigenvalue problem with this
> approach ?
>
Unfortunately, no.
Hong

>
>
>
> On Thu, Jul 3, 2014 at 8:11 AM, 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
>>>
>>
>>
>
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