[petsc-users] about ksp

[Likun Tan]

Thank you very much.

Since i have millions of such linear equations to solve, so efficiency is
my big concern.

If i keep using the uncoupled small system and use ksp to solve the linear
equations sequentially, there is nowhere i can take advantage of parallel
computing.

I think of the coupled system with the hope that the efficiency can be
improved. But it seems not a good approach.

I have tried solving the small system sequentially and it works fine, now
i need to think ways to optimize my code. Any hints on this aspect?

btw, thanks for all these communications.


On Mon, August 29, 2011 5:16 pm, Jed Brown wrote:
> On Mon, Aug 29, 2011 at 15:51, Likun Tan <likunt at andrew.cmu.edu> wrote:
>
>
>> Instead of solving Ax=b with different right-hand-side sequentially, we
>>  can also form a sparse block diagonal matrix A and a vector b composed
>> of all the elements. Then we can set values to each section of b
>> concurrently and solve the enlarged system in parallel, is this an
>> efficient way?
>>
>
> You can assemble a single AIJ matrix and then use MatCreateMAIJ() to make
> it apply to a multi-vector. You can then make a larger vector and run a
> normal Krylov method.
>
>
> The only downside is that you won't get the usual property that the
> Krylov
> method is spectrally adaptive to the right hand side (because there is
> only one inner product for all the components), but this can work alright
> anyway. Preconditioning will take more effort.
>
>
> I think this is likely premature optimization for you. I recommend
> solving the systems by calling KSPSolve() multiple times for now. Later,
> when everything is working, you might experiment with ways to solve the
> systems together.
>
>
>>
>> And also, I found MatCreateMPIBDiag()
>>
>>
>
> This format was removed from PETSc a few years ago, but I don't think
> it's what you want anyway.
>