> 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 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!cEzzrez47D-rTba54wHj2wMvjkRrPiIlyhhfvWp2H4HT4EO9-soMFVTQUt0bjRj08xqYWHXUBJusDpvvB-LqSQ$ if you are willing to share a larger example (the current Mat are extremely tiny). Thanks, Pierre > > > Best regards, > Marco > > <lsdiv.zip>
