On May 13, 2011, at 10:49 AM, David Henty wrote:
> I see in the example for how to solve A.x_i = b_i (ie multiple
> right-hand-sides for the same matrix), it simply loops over multiple separate
> KSP calls.
Correct.
>
> Wouldn't there be some benefit in having a matrix-vector routine that
> computed y_i = A.x_i for multiple "i" values?
Absolutely!
> The parallel overhead comes from communicating the off-process x values. As
> this is probably latency dominated (especially as we go to many processes),
> the comms cost of doing the communications would rise quite slowly for
> additional vectors. Likewise, the cache utilisation of the sparse A matrix
> entries would be helped by doing sevefal multiplications at once.
Completely correct.
>
> Has this already been implemented, or maybe in the pipleline?
No, no.
> Or am I somehow missing the point ...
No. You are correct that solving "multiple right hand side systems" can
offer a good improvement over solving them separately. To "do it right" with
PETSc would require a major overhaul in the PETSc "plumbing", we've never had
the resources nor the driving motivating applications to make a push in this
direction.
Barry
There is a technical sticking point that I think is non-trivial. For block
Krylov methods it can happen that the elements of the generated Krylov space at
an iteration become not linearly independent. Care has to be taken to detect
this cases properly (numerical issues of when things are linearly dependent are
potentially tricky to compute) and handle them efficiently. Presumably these
issues could be overcome with careful work.
>
> Thanks!
>
> David
>
> --
> Dr David Henty EPCC, The University of Edinburgh
> HPC Training and Support Edinburgh EH9 3JZ, UK
> d.henty at epcc.ed.ac.uk Tel: +44 (0)131 650 5960
> http://www.epcc.ed.ac.uk/~dsh/ Fax: +44 (0)131 650 6555
>
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