[petsc-users] Very poor speed up performance

[Jed Brown]

I disagree, there is easily a factor of two in flop/s between a naive
ordering (e.g. hierarchical by node type in a finite element method) and a
good low-bandwidth ordering.

This is in the FUN3D papers and still true today, in my experience.

Incomplete factorization is also very order dependent, as you note.

Jed

On Dec 22, 2010 5:03 PM, "Matthew Knepley" <knepley at gmail.com> wrote:

On Wed, Dec 22, 2010 at 10:11 AM, Yongjun Chen <yjxd.chen at gmail.com> wrote:

>
>
>
> On Wed, Dec 22, 2010 at 6:53 PM, Satish Balay <balay at mcs.anl.gov> wrote:
>>
>> On Wed, 22 De...
1) To see a large gain, the ordering you start with would have to be very
bad. Maybe it is. These
    orderings try to minimize bandwidth, which means minimize communication
in the MatMult.

2) If you use incomplete facotrization, the ordering can have a large effect
on conditioning, so
    number of iterations, which does not improve scalability. This would
impact scalability if you
   use a parallel IC, however all those packages reorder your matrix
already.

In short, I suspect this will not help a lot, except maybe with
conditioning, which is what I was refering to in the quote.

    Matt



-- 
What most experimenters take for granted before they begin their experiments
is infinitely more...
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