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 -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120821/a7ca9f40/attachment.html>
