[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?


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.


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