[petsc-dev] Can MATAIJ support block size?

[Fande Kong]

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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