[petsc-users] MatMatSolve in sequential call

[Matthew Knepley]

On Tue, Aug 21, 2012 at 11:47 AM, Jack Poulson <jack.poulson at gmail.com>wrote:

> On Tue, Aug 21, 2012 at 11:42 AM, Alexander Grayver <
> agrayver at gfz-potsdam.de> wrote:
>
>>  On 21.08.2012 18:32, Matthew Knepley wrote:
>>
>>   MUMPS takes only several minutes and 6 GB of memory to factorize it.
>>> This factorization gives residual on the order of 10e-12 and solution is
>>> indeed correct.
>>>
>>> Nevertheless, you're right, there is numerical null-space in this matrix
>>> since it comes
>>> from the discretization of equation that contains curl curl operator,
>>> but practically this
>>> case is not really the worst one.
>>>
>>
>>  This makes no sense whatsoever. How can you LU factor a matrix that has
>> a null space?
>>
>>
>> Matt,
>>
>> I'm not sure that I correctly used term numerical null-space in my post.
>> The equation is
>>
>> curl curl E + kE = -J,
>>
>> where k is a function of frequency and conductivity, whenever one of them
>> becomes small this term gets vanishingly small thus we have problems since
>> curl curl operator has nontrivial null-space by definition. So let's say
>> solving this equation for low frequencies and for models containing air is
>> difficult.
>>
>> What kind of magic is inside MUMPS I don't know, but it is able to handle
>> such cases (e.g. SuperLU and PaStiX fail).
>>
>> Also, if it matters, I'm talking about LDLt factorization in MUMPS.
>>
>> --
>> Regards,
>> Alexander
>>
>>  You can find Vasseur's talk on this exact subject here:
> http://graal.ens-lyon.fr/MUMPS/doc/ud_2010/Vasseur_talk.pdf


I was wrong, this is not nonsense. However, for curl curl the null space
grows with matrix dimension, and
as far as I can tell from the slides, the null space determination is not
scalable (Jack correct me if I am wrong).
Also, they gave no timings, so I suspect null space determination is slow.

I don't think any other LU we have will do this, so if you have null spaces
you are stuck with MUMPS.

    Matt


>
> Jack
>



-- 
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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