On Tue, Aug 21, 2012 at 3:37 PM, Matthew Knepley <knepley at gmail.com> wrote:
> 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 > > It's not something that I've studied in detail, but I believe that it isn't that the behavior will not be that different from "difficult" nonsingular cases (i.e., where a large number of pivots do not satisfy the thresholding condition and must be delayed to the parent front). If the null space is large, then I would expect this to impact performance significantly. I would expect it to make load balancing much more difficult. In practice, this might lead to nonscalability, as it is sophisticated algorithm. Jack -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120821/3e254627/attachment.html>
