<p>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.</p>
<p>This is in the FUN3D papers and still true today, in my experience.</p>
<p>Incomplete factorization is also very order dependent, as you note.</p>
<p>Jed</p>
<p><blockquote type="cite">On Dec 22, 2010 5:03 PM, "Matthew Knepley" <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<br><br><p><font color="#500050">On Wed, Dec 22, 2010 at 10:11 AM, Yongjun Chen <<a href="mailto:yjxd.chen@gmail.com">yjxd.chen@gmail.com</a>> wrote:</font></p>
<div class="gmail_quote"><p><font color="#500050">><br>><br>><br>> On Wed, Dec 22, 2010 at 6:53 PM, Satish Balay <<a href="mailto:balay@mcs.anl.gov">balay@mcs.anl.gov</a>> wrote:<br>>><br>>> On Wed, 22 De...</font></p>
<div>1) To see a large gain, the ordering you start with would have to be very bad. Maybe it is. These</div>
<div> orderings try to minimize bandwidth, which means minimize communication in the MatMult.</div><div><br></div><div>2) If you use incomplete facotrization, the ordering can have a large effect on conditioning, so</div>
<div> number of iterations, which does not improve scalability. This would impact scalability if you</div><div> use a parallel IC, however all those packages reorder your matrix already.</div><div><br></div><div>In short, I suspect this will not help a lot, except maybe with conditioning, which is what I was refering to in the quote.</div>
<div><br></div><div> Matt</div><div> </div></div><p><font color="#500050"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more...</font></p></blockquote></p>