[petsc-users] MatMatSolve in sequential call
Alexander Grayver
agrayver at gfz-potsdam.de
Tue Aug 21 11:42:02 CDT 2012
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
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