[petsc-dev] Can MATAIJ support block size?

[Fande Kong]

In order to make the discussion simple, we can just assume the sparse block
is a diagonal matrix. How to take the advantage of the diagonal block
matrix?

Fande,

On Thu, Sep 20, 2018 at 12:28 PM Fande Kong <fdkong.jd at gmail.com> wrote:

>
>
> On Thu, Sep 20, 2018 at 12:09 PM Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Thu, Sep 20, 2018 at 1:26 PM Fande Kong <fdkong.jd at gmail.com> wrote:
>>
>>> Hi Developers,
>>>
>>> MATBAIJ actually assumes that the point-block is dense. It is fine if
>>> the block size is small for example less than 50, but we may suffer from a
>>> memory issue if the block is large such as 1000. The block is not necessary
>>> dense. In my application, neutron transport equations, the block is
>>> actually sparse (coming from direction and energy grids).  Now I am using
>>> MATAIJ, but I want to take into consideration there are many variables on
>>> each spatial grid when doing some ILU(0).  ILU(0) is used as a subdomain
>>> solver for ASM and BJACOBI.
>>>
>>> I would like to support point-block ILU(0) in MATAIJ (not MATBAIJ)
>>> because the block is sparse. Any comments? It is worthwhile to do that? I
>>> think we might reduce the symbolic factor time when considering the block.
>>>
>>
>> What optimization do you hope to take advantage of?
>>
>
> The inverse of sparse block can be approximated with the inverse of the
> block diagonal.
>
> Does it help reduce the compute time in symbolic factorization?
>
> Fande,
>
>
>> The main optimization in sparse LU is finding dense blocks,
>> and it should do a good job of that. I do not see what defining huge,
>> sparse blocks does for you.
>>
>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> Thanks,
>>>
>>> Fande,
>>>
>>
>>
>> --
>> 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
>>
>> https://www.cse.buffalo.edu/~knepley/
>> <http://www.cse.buffalo.edu/~knepley/>
>>
>
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