I implemented the Grundmann-Möller rules for some general dimensional FEM stuff a while back. My observations were along these lines also. The other issue is that they are not going to behave as nicely against some arbitrary function; I forget exactly how the lebesgue constants work out, but it isn't necessarily as good as the conical rules. The conical rules also tended to win at low-order in 2D; it was 3D and above where the more elegant rules tended to win.
My previous declaration that this should be done got stuck in an FFC/FIAT limbo. - Peter On Tue, Jun 22, 2010 at 11:18 AM, Andy Ray Terrel <[email protected]>wrote: > On Tue, Jun 22, 2010 at 10:31 AM, Garth N. Wells <[email protected]> wrote: > > > > > > On 22/06/10 07:05, Andy Ray Terrel wrote: > >> > >> On Tue, Jun 22, 2010 at 6:15 AM, Anders Logg<[email protected]> wrote: > >>> > >>> On Tue, Jun 22, 2010 at 01:04:27PM +0200, Kristian Oelgaard wrote: > >>>> > >>>> On 21 June 2010 23:16, Kent Andre<[email protected]> 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} > >> } > >> > > > > I've pasted the above into > > > > https://blueprints.launchpad.net/ffc/+spec/simplex-quad > > > > Garth > > > > I added a few more notes and links on the blueprint. > > -- Andy > > >>> > >>> -- > >>> Anders > >>> > >>> -----BEGIN PGP SIGNATURE----- > >>> Version: GnuPG v1.4.10 (GNU/Linux) > >>> > >>> iEYEARECAAYFAkwgmzsACgkQTuwUCDsYZdGcqwCgh1QCnNr0Jr1a2mcxDqheCpZ0 > >>> ItkAn36nLWyr2RDO6pqgF4PX753ItHaU > >>> =HnEK > >>> -----END PGP SIGNATURE----- > >>> > >>> _______________________________________________ > >>> Mailing list: https://launchpad.net/~ffc<https://launchpad.net/%7Effc> > >>> Post to : [email protected] > >>> Unsubscribe : https://launchpad.net/~ffc<https://launchpad.net/%7Effc> > >>> More help : https://help.launchpad.net/ListHelp > >>> > >>> > >> > >> _______________________________________________ > >> Mailing list: https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > >> Post to : [email protected] > >> Unsubscribe : https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > >> More help : https://help.launchpad.net/ListHelp > > > > _______________________________________________ > > Mailing list: https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > > Post to : [email protected] > > Unsubscribe : https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > > More help : https://help.launchpad.net/ListHelp > > > > _______________________________________________ > Mailing list: https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > Post to : [email protected] > Unsubscribe : https://launchpad.net/~ffc <https://launchpad.net/%7Effc> > More help : https://help.launchpad.net/ListHelp >
_______________________________________________ Mailing list: https://launchpad.net/~ffc Post to : [email protected] Unsubscribe : https://launchpad.net/~ffc More help : https://help.launchpad.net/ListHelp
