[petsc-dev] Can MATAIJ support block size?

Fande Kong fdkong.jd at gmail.com
Thu Sep 20 13:28:32 CDT 2018

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?


> 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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