Great thanks, Matt! The second option is what I was looking for.
Best Regards, Vlad ________________________________ От: Matthew Knepley <knep...@gmail.com> Отправлено: 10 ноября 2021 г. 16:45:00 Кому: Vladislav Pimanov Копия: petsc-users@mcs.anl.gov Тема: Re: [petsc-users] How to compute the condition number of SchurComplementMat preconditioned with PCSHELL. On Wed, Nov 10, 2021 at 8:42 AM Vladislav Pimanov <vladislav.pima...@skoltech.ru<mailto:vladislav.pima...@skoltech.ru>> wrote: Dear PETSc community, I wonder if you could give me a hint on how to compute the condition number of a preconditioned matrix in a proper way. I have a MatSchurComplement matrix S and a preconditioner P of the type PCSHELL (P is a diffusion matrix, which itself is inverted by KSPCG). I tried to compute the condition number of P^{-1}S "for free" during the outer PCG procedure using KSPComputeExtremeSingularValues() routine. Unfortunately, \sigma_min does not converge even if the solution is computed with very high precision. I also looked at SLEPc interface, but did not realised how PC should be included. You can do this at least two ways: 1) Make a MatShell for P^{-1} S. This is easy, but you will not be able to use any factorization-type PC on that matrix. 2) Solve instead the generalized EVP, S x = \lambda P x. Since you already have P^{-1}, this should work well. Thanks, Matt Thanks! Sincerely, Vladislav Pimanov -- 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 https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
