> On 7 May 2024, at 9:10 AM, Marco Seiz <ma...@kit.ac.jp> wrote: > > Thanks for the quick response! > > On 07.05.24 14:24, Pierre Jolivet wrote: >> >> >>> On 7 May 2024, at 7:04 AM, Marco Seiz <ma...@kit.ac.jp> wrote: >>> >>> This Message Is From an External Sender >>> This message came from outside your organization. >>> Hello, >>> >>> something a bit different from my last question, since that didn't >>> progress so well: >>> I have a related model which generally produces a rectangular matrix A, >>> so I am using LSQR to solve the system. >>> The matrix A has two nonzeros (1, -1) per row, with A^T A being similar >>> to a finite difference Poisson matrix if the rows were permuted randomly. >>> The problem is singular in that the solution is only specified up to a >>> constant from the matrix, with my target solution being a weighted zero >>> average one, which I can handle by adding a nullspace to my matrix. >>> However, I'd also like to pin (potentially many) DOFs in the future so I >>> also tried pinning a single value, and afterwards subtracting the >>> average from the KSP solution. >>> This leads to the KSP *sometimes* diverging when I use a preconditioner; >>> the target size of the matrix will be something like ([1,20] N) x N, >>> with N ~ [2, 1e6] so for the higher end I will require a preconditioner >>> for reasonable execution time. >>> >>> For a smaller example system, I set up my application to dump the input >>> to the KSP when it breaks down and I've attached a simple python script >>> + data using petsc4py to demonstrate the divergence for those specific >>> systems. >>> With `python3 lsdiv.py -pc_type lu -ksp_converged_reason` that >>> particular system shows breakdown, but if I remove the pinned DOF and >>> add the nullspace (pass -usens) it converges. I did try different PCs >>> but they tend to break down at different steps, e.g. `python3 lsdiv.py >>> -usenormal -qrdiv -pc_type qr -ksp_converged_reason` shows the breakdown >>> for PCQR when I use MatCreateNormal for creating the PC mat, but >>> interestingly it doesn't break down when I explicitly form A^T A (don't >>> pass -usenormal). >> >> What version are you using? All those commands are returning >> Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1 >> So I cannot reproduce any breakdown, but there have been recent changes to >> KSPLSQR. > For those tests I've been using PETSc 3.20.5 (last githash was > 4b82c11ab5d ). > I pulled the latest version from gitlab ( 6b3135e3cbe ) and compiled it, > but I had to drop --download-suitesparse=1 from my earlier config due to > errors. > Should I write a separate mail about this? > > The LU example still behaves the same for me (`python3 lsdiv.py -pc_type > lu -ksp_converged_reason` gives DIVERGED_BREAKDOWN, `python3 lsdiv.py > -usens -pc_type lu -ksp_converged_reason` gives CONVERGED_RTOL_NORMAL) > but the QR example fails since I had to remove suitesparse. > petsc4py.__version__ reports 3.21.1 and if I rebuild my application, > then `ldd app` gives me `libpetsc.so > <https://urldefense.us/v3/__http://libpetsc.so/__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScugHRUKcQ$ > >.3.21 => > /opt/petsc/linux-c-opt/lib/libpetsc.so > <https://urldefense.us/v3/__http://libpetsc.so/__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScugHRUKcQ$ > >.3.21` so it should be using the > newly built one. > The application then still eventually yields a DIVERGED_BREAKDOWN. > I don't have a ~/.petscrc and PETSC_OPTIONS is unset, so if we are on > the same version and there's still a discrepancy it is quite weird.
Quite weird indeed… $ python3 lsdiv.py -pc_type lu -ksp_converged_reason Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1 $ python3 lsdiv.py -usens -pc_type lu -ksp_converged_reason Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1 $ python3 lsdiv.py -pc_type qr -ksp_converged_reason Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1 $ python3 lsdiv.py -usens -pc_type qr -ksp_converged_reason Linear solve converged due to CONVERGED_RTOL_NORMAL iterations 1 >>> For the moment I can work by adding the nullspace but eventually the >>> need for pinning DOFs will resurface, so I'd like to ask where the >>> breakdown is coming from. What causes the breakdowns? Is that a generic >>> problem occurring when adding (dof_i = val) rows to least-squares >>> systems which prevents these preconditioners from being robust? If so, >>> what preconditioners could be robust? >>> I did a minimal sweep of the available PCs by going over the possible >>> inputs of -pc_type for my application while pinning one DOF. Excepting >>> unavailable PCs (not compiled for, other setup missing, ...) and those >>> that did break down, I am left with ( hmg jacobi mat none pbjacobi sor >>> svd ). >> It’s unlikely any of these preconditioners will scale (or even converge) for >> problems with up to 1E6 unknowns. >> I could help you setup >> https://urldefense.us/v3/__https://epubs.siam.org/doi/abs/10.1137/21M1434891__;!!G_uCfscf7eWS!auri5B6VaP-JYC4fuoLQd6QGnMRYi45UVg6GvK8V2FIlWo6HdPSPwjqjQnRiV2HkM5lAHgRRgpwXScvk6kPrWA$ >> if you are willing to share a larger example (the current Mat are >> extremely tiny). > Yes, that would be great. About how large of a matrix do you need? I can > probably quickly get something non-artificial up to O(N) ~ 1e3, That’s big enough. If you’re in luck, AMG on the normal equations won’t behave too badly, but I’ll try some more robust (in theory) methods nonetheless. Thanks, Pierre > bigger > matrices will take some time since I purposefully ignored MPI previously. > The matrix basically describes the contacts between particles which are > resolved on a uniform grid, so the main memory hog isn't the matrix but > rather resolving the particles. > I should mention that the matrix changes over the course of the > simulation but stays constant for many solves, i.e. hundreds to > thousands of solves with variable RHS between periods of contact > formation/loss. > >> >> Thanks, >> Pierre >>> >>> >>> Best regards, >>> Marco >>> >>> <lsdiv.zip> >> >> > Best regards, > Marco