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.

There is no doubt that this difference can exist, but many mesh generators (such as triangle) give back a good

ordering. FUN3D used an inexplicably bad ordering.

Matt

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

Jed

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

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

>
>
>
> On Wed, Dec 22, 2010 at 6:53 PM, Satish Balay <balay@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...