[petsc-dev] Fwd: [mumps-dev] support for distributed right-hand vectors?

[Jack Poulson]

I can't help but interject. Sparse direct solvers are not nonscalable "in
general". General purpose solvers have to worry about pivoting, which
greatly complicates the factorization and tends to get in the way of
scalability. Several sparse-direct solvers use one-dimensional frontal
distributions (e.g., MUMPS and SPOOLES) in order to simplify pivoting,
though MUMPS uses a two-dimensional distribution at the root front.

It is well-known how to make multifrontal Cholesky factorization scalable
(for example, see one of the many papers by Gupta/Karypis/Kumar/Joshi from
the 90's). Making multifrontal triangular solves scalable is another matter.

Jack

On Tue, Nov 13, 2012 at 6:49 AM, Alexander Grayver
<agrayver at gfz-potsdam.de>wrote:

> On 12.11.2012 21:19, Hong Zhang wrote:
>
>> Alexander:
>>
>> Interesting results!
>> Do you use the same matrix ordering?
>> The ordering might affect memory and execution time.
>>
>
> Hong,
>
> I used ptscotch for both of them.
>
>
>
>> The algorithms of direct solver are in general non-scalable, both
>> in-terms of
>> flops and memory. However, I'm surprised by the rate of memory growth
>> for both solvers. I would suggest sending your report to the PaStiX
>> and MUMPS developers who can give better explanations, as well as
>> provide improved implementations.
>>
>
> I will consider this, thank you.
>
> --
> Regards,
> Alexander
>
>
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