On Tue, Aug 21, 2012 at 11:47 AM, Jack Poulson <jack.poulson at gmail.com>wrote:
> On Tue, Aug 21, 2012 at 11:42 AM, Alexander Grayver < > agrayver at gfz-potsdam.de> wrote: > >> On 21.08.2012 18:32, Matthew Knepley wrote: >> >> MUMPS takes only several minutes and 6 GB of memory to factorize it. >>> This factorization gives residual on the order of 10e-12 and solution is >>> indeed correct. >>> >>> Nevertheless, you're right, there is numerical null-space in this matrix >>> since it comes >>> from the discretization of equation that contains curl curl operator, >>> but practically this >>> case is not really the worst one. >>> >> >> This makes no sense whatsoever. How can you LU factor a matrix that has >> a null space? >> >> >> Matt, >> >> I'm not sure that I correctly used term numerical null-space in my post. >> The equation is >> >> curl curl E + kE = -J, >> >> where k is a function of frequency and conductivity, whenever one of them >> becomes small this term gets vanishingly small thus we have problems since >> curl curl operator has nontrivial null-space by definition. So let's say >> solving this equation for low frequencies and for models containing air is >> difficult. >> >> What kind of magic is inside MUMPS I don't know, but it is able to handle >> such cases (e.g. SuperLU and PaStiX fail). >> >> Also, if it matters, I'm talking about LDLt factorization in MUMPS. >> >> -- >> Regards, >> Alexander >> >> You can find Vasseur's talk on this exact subject here: > http://graal.ens-lyon.fr/MUMPS/doc/ud_2010/Vasseur_talk.pdf I was wrong, this is not nonsense. However, for curl curl the null space grows with matrix dimension, and as far as I can tell from the slides, the null space determination is not scalable (Jack correct me if I am wrong). Also, they gave no timings, so I suspect null space determination is slow. I don't think any other LU we have will do this, so if you have null spaces you are stuck with MUMPS. Matt > > Jack > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120821/fc768b05/attachment.html>
