On Tue, Jun 22, 2010 at 6:15 AM, Anders Logg<logg@xxxxxxxxx> wrote:
On Tue, Jun 22, 2010 at 01:04:27PM +0200, Kristian Oelgaard wrote:
On 21 June 2010 23:16, Kent Andre<kent-and@xxxxxxxxx> wrote:
Strange. I used dorsal to compile the dev versions of the various
packages. Dolfin, ffc, and sfc are only a few days old.
But do you have any suggestions for how to optimize the FFC generated
code ? I have used quadrature here, tensor representation is not good
in this application.
I had a look at the generated code from FFC and SyFi
(which by the way is a real pain when PyDOLFIN is involved)
and realised that your comparison is not fair.
FFC uses the UFL algorithm estimate_total_polynomial_degree() to
compute the quadrature_degree.
SFC uses (in this case) the UFL algorithm estimate_quadrature_degree()
which is less conservative.
This results in FFC using 25 integration points to compute the
integral while SFC just uses 3.
If you use the option:
parameters ["form_compiler"]["quadrature_degree"] = "2"
the comparison is _more_ fair and the numbers are almost the same.
SFC still uses 3 points, while FFC now uses 4 points which leads to my
answer to your first question:
"How should I optimize FFC?" :)
https://blueprints.launchpad.net/ffc/+spec/simplex-quadrature
I think either Andy Terrel or Peter Brune mentioned having worked out
some code for computing more efficient quadrature on simplices. There
was some discussion on adding that either to FIAT or FFC.
What ever happened to that?
The only fast quadrature I was working on was for the BCR wavelet
rules for Calderon Zygmund operators. Rob has some recent stuff on
fast quadrature using Bernstein basis. I'm not sure what Peter might
have been doing.
The local expert on quadrature at TACC, tells me the fastest schemes
for quadrature for simplices is Grundmann-Möller for lower orders (<
20 ish) and the standard conical product for higher orders.
@article{grundmann:282,
author = {Axel Grundmann and H. M. M\"{o}ller},
collaboration = {},
title = {Invariant Integration Formulas for the $n$-Simplex by
Combinatorial Methods},
publisher = {SIAM},
year = {1978},
journal = {SIAM Journal on Numerical Analysis},
volume = {15},
number = {2},
pages = {282-290},
url = {http://link.aip.org/link/?SNA/15/282/1},
doi = {10.1137/0715019}
}
