[petsc-users] MatMatSolve in sequential call

[Jack Poulson]

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

Jack
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