[petsc-users] Reasons for breakdown in preconditioned LSQR

Tue May 7 07:02:27 CDT 2024

On Tue, May 7, 2024 at 5:12 AM Pierre Jolivet <pierre at joliv.et> wrote:

> On 7 May 2024, at 9: 10 AM, Marco Seiz <marco@ 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 <marco@ kit. ac. jp> wrote: This
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> On 7 May 2024, at 9:10 AM, Marco Seiz <marco at 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 <marco at kit.ac.jp> wrote:
>
> This Message Is From an External Sender
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> 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!fB-MI7viuwcYPEUg4w1S4_woxMQH7Kg5wnygmQdQdtqlCY5hQY4bFmFI3dJtuNZX9R-0i_z0Hq4eR73CPbQx$ 
> <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.
>

We have also had good luck forming and factoring a block diagonal
approximation of the normal equations. It depends on your problem. What is
this problem?

  Thanks,

     Matt

> 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
>
>
>

-- 
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!fB-MI7viuwcYPEUg4w1S4_woxMQH7Kg5wnygmQdQdtqlCY5hQY4bFmFI3dJtuNZX9R-0i_z0Hq4eRzQ_nPK6$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!fB-MI7viuwcYPEUg4w1S4_woxMQH7Kg5wnygmQdQdtqlCY5hQY4bFmFI3dJtuNZX9R-0i_z0Hq4eR-ODWjrB$ >
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