[petsc-users] Strange strong scaling result

[Ce Qin]

>
>>> 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.

Best,
Ce
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