[petsc-users] Strange strong scaling result

[Matthew Knepley]

On Tue, Jul 12, 2022 at 7:32 AM Ce Qin <qince168 at gmail.com> wrote:

>
>
>>>> The linear system is complex-valued. We rewrite it into its real form
>>>> and solve it using FGMRES and an optimal block-diagonal preconditioner.
>>>> We use CG and the AMS preconditioner implemented in HYPRE to solve the
>>>> smaller real linear system arised from applying the block
>>>> preconditioner.
>>>> The iteration number of FGMRES and CG keep almost constant in all the
>>>> runs.
>>>>
>>>
>>> So those blocks decrease in size as you add more processes?
>>>
>>>
>>
> I am sorry for the unclear description of the block-diagonal
> preconditioner.
> Let K be the original complex system matrix, A = [Kr, -Ki; -Ki, -Kr] is
> the equivalent
> real form of K. Let P = [Kr+Ki, 0; 0, Kr+Ki], it can beproved that P is an
> optimal
> preconditioner for A. In our implementation, only Kr, Ki and Kr+Ki
> are explicitly stored as MATMPIAIJ. We use MATSHELL to represent A and P.
> We use FGMRES + P to solve Ax=b, and CG + AMS to
> solve (Kr+Ki)y=c. So the block size is never changed.
>

Then we have to break down the timings further. I suspect AMS is not taking
as long, since
all other operations scale like N.

  Thanks,

     Matt



> Best,
> Ce
>
-- 
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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