[petsc-dev] Jack has produced a scalable sparse direct solver

[Jack Poulson]

Hi Hong,

On Mon, Jul 23, 2012 at 11:53 AM, Hong Zhang <hzhang at mcs.anl.gov> wrote:

> Jack:
>
>>
>> I'm getting started on creating documentation right now; it should end up
>> looking very similar to Elemental's.
>>
>
> The detailed instruction will be very helpful, especially
> the sparse matrix data structures. Notify us when the documentation is out.
>

Will do. I just pushed out documentation for the build system:
http://poulson.github.com/Clique/build.html

The rest should follow soon.


> Is this a sparse Cholesky direct solver?
>

More or less. It currently supports LDL^T and LDL^H factorizations without
pivoting, and the latter certainly works for Hermitian positive-definite
matrices. The current implementation is slightly more general than Cholesky
and should achieve roughly the same performance.


> Currently, only mumps supports parallel sparse Cholesky direct solver.
> Yours will be a good addition to the petsc external solvers.
>

Thanks! I'll do my best to help with the integration when the time comes.


>
>> Please keep in mind that there is not _yet_ any support for pivoting, as
>> I needed Clique's functionality for indefinite complex symmetric matrices
>> which are nice enough to be factored accurately without pivoting.
>
>
> Petsc users likely use it as a preconditioner.
> In case of zero pivot, you may provide a routine/option for adding a small
> shift?
>

Yes, that is what I was thinking. For instance, for Helmholtz equations,
one can get away with very small positive imaginary shifts (the physically
corresponds to slightly damping waves).


>
>> Clique's nested dissection is built on top of a nodal graph bisection
>> routine which uses a custom interface to parmetis; I suspect that the graph
>> partitioning is currently the least scalable part of the black-box
>> interface due to KLFM refinement being so hard to parallelize.
>
>
> Xuan has almost finished the petsc-elemental interface
> (see petsc-dev/src/mat/impls/elemental/).
> We would appreciate if you can take a look at it and give us
> your comments/suggests.
>
>
I just took a quick look and will make time to go over it in detail later
today. I'll send out patch if I have any concrete suggestions.

Jack


>>
>> On Mon, Jul 23, 2012 at 10:12 AM, Hong Zhang <hzhang at mcs.anl.gov> wrote:
>>
>>> Xuan will take a look at this.
>>> Hong
>>>
>>> On Mon, Jul 23, 2012 at 9:47 AM, Matthew Knepley <knepley at gmail.com>wrote:
>>>
>>>> I think we just need a small converter from AIJ:
>>>>
>>>>
>>>> https://bitbucket.org/poulson/clique/src/dc417c7e9403/tests/DistSparseMatrix.cpp
>>>>
>>>>   Matt
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>
>>>
>>
>
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