[petsc-users] Setting up MUMPS in PETSc

[Hong Zhang]

Clique-petsc interface does not work yet.
Things need to be done:
- reuse symbolic factor (Jack added this feature several weeks ago, but I
do not have time work on it yet)
- distributed rhs and solution vector (not sure about clique's status)

Jinquan: did you use Cholesky or LU from mumps?
For symmetric problem, use mumps Cholesky.

Hong


On Tue, Oct 23, 2012 at 4:14 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> On Tue, Oct 23, 2012 at 2:48 PM, Jinquan Zhong <jzhong at scsolutions.com>wrote:
>
>> >> Soil-structure interaction.
>>
>
> Why is it dense? Is it effectively the solution of another equation? An
> integral operator?
>
>
>>
>>
>> **
>>
>> The amount of fill depends on the size of minimal vertex separators.
>> Sparse matrices with the same number of nonzeros and same number of
>> nonzeros per row can have vertex separators that are orders of magnitude
>> different in size. The fill is quadratic in the size of the separators and
>> computation is cubic.****
>>
>> >> Could you be more specific?  I am not quite with you yet.
>>
>
> A 10x10x10000 3D problem with hex elements has about 1M dofs and about 27
> nonzeros per row. The minimal vertex separator consists of 10^2 vertices,
> so the final dense matrix is 100x100. The direct solver is extremely fast
> for this problem.
>
> A 100x100x100 3D problem has the same number of dofs and nonzeros per row.
> The minimal vertex separator is 100^2 vertices, so the final dense matrix
> is 10000x10000 (and there are many pretty big dense matrices to get there).
> This problem requires on the order of 10000 times as much memory and
> 1000000 times as many flops.
>
> If we switch from a FEM discretization to a FD discretization with a
> stencil width of 3, the vertex separator grows by a factor of 3, increasing
> memory usage by a factor of 9 and flops by a factor of 27. If you replace
> that high order system with high order continuous Galerkin FEM using larger
> elements so the number of dofs is constant, the number of nonzeros in the
> matrix may grow, but the vertex separators go back to being the same as the
> original problem.
>
>
>> ****
>>
>> ** **
>>
>> Is your problem symmetric?****
>>
>> ** **
>>
>> >> Yes.
>>
>
> Hong, is the Clique code in petsc-dev ready to use?
>
> There is no reason we should keep spending time dealing with MUMPS quirks
> and scalability problems on symmetric problems.
>
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