Thankfully for this step, the matrix is not dense. But thank you.
Nidish On 8/17/20 8:52 AM, Jose E. Roman wrote:
El 17 ago 2020, a las 14:27, Barry Smith <bsm...@petsc.dev> escribió: Nidish, Your matrix is dense, correct? MUMPS is for sparse matrices. Then I guess you could use Scalapack http://netlib.org/scalapack/slug/node48.html#SECTION04323200000000000000 to do the SVD. The work is order N^3 and parallel efficiency may not be great but it might help you solve your problem. I don't know if SLEPc has an interface to Scalapack for SVD or not.Yes, SLEPc (master) has interfaces for ScaLAPACK and Elemental for both SVD and (symmetric) eigenvalues. JoseBarryOn Aug 17, 2020, at 2:51 AM, Jose E. Roman <jro...@dsic.upv.es> wrote: You can use SLEPc's SVD to compute the nullspace, but it has pitfalls: make sure you use an absolute convergence test (not relative); for the particular case of zero singular vectors, accuracy may not be very good and convergence may be slow (with the corresponding high computational cost). MUMPS has functionality to get a basis of the nullspace, once you have computed the factorization. But I don't know if this is easily accessible via PETSc. JoseEl 17 ago 2020, a las 3:10, Nidish <n...@rice.edu> escribió: Oh damn. Alright, I'll keep trying out the different options. Thank you, Nidish On 8/16/20 8:05 PM, Barry Smith wrote:SVD is enormously expensive, needs to be done on a full dense matrix so completely impractical. You need the best tuned iterative method, Jose is the by far the most knowledgeable about that. BarryOn Aug 16, 2020, at 7:46 PM, Nidish <n...@rice.edu> wrote: Thank you for the suggestions. I'm getting a zero pivot error for the LU in slepc while calculating the rest of the modes. Would conducting an SVD for just the stiffness matrix and then using the singular vectors as bases for the nullspace work? I haven't tried this out just yet, but I'm wondering if you could provide me insights into whether this will. Thanks, Nidish On 8/16/20 2:50 PM, Barry Smith wrote:If you know part of your null space explicitly (for example the rigid body modes) I would recommend you always use that information explicitly since it is extremely expensive numerically to obtain. Thus rather than numerically computing the entire null space compute the part orthogonal to the part you already know. Presumably SLEPc has tools to help do this, naively I would just orthogonalized against the know subspace during the computational process but there are probably better ways. BarryOn Aug 16, 2020, at 11:26 AM, Nidish <n...@rice.edu> wrote: Well some of the zero eigenvectors are rigid body modes, but there are some more which are introduced by lagrange-multiplier based constraint enforcement, which are non trivial. My final application is for a nonlinear simulation, so I don't mind the extra computational effort initially. Could you have me the suggested solver configurations to get this type of eigenvectors in slepc? Nidish On Aug 16, 2020, at 00:17, Jed Brown <j...@jedbrown.org> wrote: It's possible to use this or a similar algorithm in SLEPc, but keep in mind that it's more expensive to compute these eigenvectors than to solve a linear system. Do you have a sequence of systems with the same null space? You referred to the null space as "rigid body modes". Why can't those be written down? Note that PETSc has convenience routines for computing rigid body modes from coordinates. Nidish < n...@rice.eduwrites:I just use the standard eigs function (https://www.mathworks.com/help/matlab/ref/eigs.html ) as a black box. I think it uses a lanczos type method under the hood. Nidish On Aug 15, 2020, 21:42, at 21:42, Barry Smith < bsm...@petsc.devwrote:Exactly what algorithm are you using in Matlab to get the 10 smallest eigenvalues and their corresponding eigenvectors? Barry On Aug 15, 2020, at 8:53 PM, Nidish <n...@rice.eduwrote:The section on solving singular systems in the manual starts with assuming that the singular eigenvectors are already known. I have a large system where finding the singular eigenvectors is not trivially written down. How would you recommend I proceed with making initial estimates? In MATLAB (with MUCH smaller matrices), I conduct an eigensolve for the first 10 smallest eigenvalues and take the eigenvectors corresponding to the zero eigenvalues from this. This approach doesn't work here since I'm unable to use SLEPc for solving K.v = lam*M.v for cases where K is positive semi-definite (contains a few "rigid body modes") and M is strictly positive definite. I'd appreciate any assistance you may provide with this. Thank you, Nidish-- Nidish-- Nidish
-- Nidish
