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 Jack -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120821/2e7563ea/attachment.html>
