[petsc-users] Questions Regarding PETSc and Solving Constrained Structural Mechanics Problems
Matthew Knepley
knepley at gmail.com
Mon Jun 16 05:40:10 CDT 2025
On Sun, Jun 15, 2025 at 9:46 PM hexioafeng <hexiaofeng at buaa.edu.cn> wrote:
> Hello,
>
> Here are the options and outputs:
>
> options:
>
> -ksp_type cg -pc_type gamg -pc_gamg_parallel_coarse_grid_solver
> -pc_fieldsplit_detect_saddle_point -pc_fieldsplit_type schur
> -pc_fieldsplit_schur_precondition selfp
> -fieldsplit_1_mat_schur_complement_ainv_type lump
> -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly
> -fieldsplit_0_pc_type gamg -fieldsplit_0_mg_coarse_pc_type_type svd
> -fieldsplit_1_ksp_type preonly -fieldsplit_1_pc_type bjacobi
> -fieldsplit_1_sub_pc_type sor -ksp_view -ksp_monitor_true_residual
> -ksp_converged_reason -fieldsplit_0_mg_levels_ksp_monitor_true_residual
> -fieldsplit_0_mg_levels_ksp_converged_reason
> -fieldsplit_1_ksp_monitor_true_residual
> -fieldsplit_1_ksp_converged_reason
>
This option was wrong:
-fieldsplit_0_mg_coarse_pc_type_type svd
from the output, we can see that it should have been
-fieldsplit_0_mg_coarse_sub_pc_type_type svd
THanks,
Matt
> output:
>
> 0 KSP unpreconditioned resid norm 2.777777777778e+01 true resid norm
> 2.777777777778e+01 ||r(i)||/||b|| 1.000000000000e+00
> Linear solve did not converge due to DIVERGED_PC_FAILED iterations 0
> PC failed due to SUBPC_ERROR
> KSP Object: 1 MPI processes
> type: cg
> maximum iterations=200, initial guess is zero
> tolerances: relative=1e-06, absolute=1e-12, divergence=1e+30
> left preconditioning
> using UNPRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: gamg
> type is MULTIPLICATIVE, levels=2 cycles=v
> Cycles per PCApply=1
> Using externally compute Galerkin coarse grid matrices
> GAMG specific options
> Threshold for dropping small values in graph on each level =
> Threshold scaling factor for each level not specified = 1.
> AGG specific options
> Symmetric graph false
> Number of levels to square graph 1
> Number smoothing steps 1
> Complexity: grid = 1.00176
> Coarse grid solver -- level -------------------------------
> KSP Object: (mg_coarse_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (mg_coarse_) 1 MPI processes
> type: bjacobi
> number of blocks = 1
> Local solver is the same for all blocks, as in the following KSP
> and PC objects on rank 0:
> KSP Object: (mg_coarse_sub_) 1 MPI processes
> type: preonly
> maximum iterations=1, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (mg_coarse_sub_) 1 MPI processes
> type: lu
> out-of-place factorization
> tolerance for zero pivot 2.22045e-14
> using diagonal shift on blocks to prevent zero pivot [INBLOCKS]
> matrix ordering: nd
> factor fill ratio given 5., needed 1.
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=7, cols=7
> package used to perform factorization: petsc
> total: nonzeros=45, allocated nonzeros=45
> using I-node routines: found 3 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=7, cols=7
> total: nonzeros=45, allocated nonzeros=45
> total number of mallocs used during MatSetValues calls=0
> using I-node routines: found 3 nodes, limit used is 5
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=7, cols=7
> total: nonzeros=45, allocated nonzeros=45
> total number of mallocs used during MatSetValues calls=0
> using nonscalable MatPtAP() implementation
> using I-node (on process 0) routines: found 3 nodes, limit used
> is 5
> Down solver (pre-smoother) on level 1 -------------------------------
> KSP Object: (mg_levels_1_) 1 MPI processes
> type: chebyshev
> eigenvalue estimates used: min = 0., max = 0.
> eigenvalues estimate via gmres min 0., max 0.
> eigenvalues estimated using gmres with translations [0. 0.1; 0.
> 1.1]
> KSP Object: (mg_levels_1_esteig_) 1 MPI processes
> type: gmres
> restart=30, using Classical (unmodified) Gram-Schmidt
> Orthogonalization with no iterative refinement
> happy breakdown tolerance 1e-30
> maximum iterations=10, initial guess is zero
> tolerances: relative=1e-12, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: (mg_levels_1_) 1 MPI processes
> type: sor
> type = local_symmetric, iterations = 1, local iterations = 1,
> omega = 1.
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=624, cols=624
> total: nonzeros=25536, allocated nonzeros=25536
> total number of mallocs used during MatSetValues calls=0
> using I-node (on process 0) routines: found 336 nodes, limit
> used is 5
> estimating eigenvalues using noisy right hand side
> maximum iterations=2, nonzero initial guess
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (mg_levels_1_) 1 MPI processes
> type: sor
> type = local_symmetric, iterations = 1, local iterations = 1,
> omega = 1. linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=624, cols=624
> total: nonzeros=25536, allocated nonzeros=25536
> total number of mallocs used during MatSetValues calls=0
> using I-node (on process 0) routines: found 336 nodes, limit
> used is 5 Up solver (post-smoother) same as down solver (pre-smoother)
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=624, cols=624
> total: nonzeros=25536, allocated nonzeros=25536
> total number of mallocs used during MatSetValues calls=0
> using I-node (on process 0) routines: found 336 nodes, limit used is
> 5
>
>
> Best regards,
>
> Xiaofeng
>
>
> On Jun 14, 2025, at 07:28, Barry Smith <bsmith at petsc.dev> wrote:
>
>
> Matt,
>
> Perhaps we should add options -ksp_monitor_debug and
> -snes_monitor_debug that turn on all possible monitoring for the (possibly)
> nested solvers and all of their converged reasons also? Note this is not
> completely trivial because each preconditioner will have to supply its list
> based on the current solver options for it.
>
> Then we won't need to constantly list a big string of problem specific
> monitor options to ask the user to use.
>
> Barry
>
>
>
>
> On Jun 13, 2025, at 9:09 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Thu, Jun 12, 2025 at 10:55 PM hexioafeng <hexiaofeng at buaa.edu.cn>
> wrote:
>
>> Dear authors,
>>
>> I tried *-pc_type game -pc_gamg_parallel_coarse_grid_solver* and *-pc_type
>> field split -pc_fieldsplit_detect_saddle_point -fieldsplit_0_ksp_type
>> pronely -fieldsplit_0_pc_type game -fieldsplit_0_mg_coarse_pc_type sad
>> -fieldsplit_1_ksp_type pronely -fieldsplit_1_pc_type Jacobi
>> _fieldsplit_1_sub_pc_type for* , both options got the
>> KSP_DIVERGE_PC_FAILED error.
>>
>
> With any question about convergence, we need to see the output of
>
> -ksp_view -ksp_monitor_true_residual -ksp_converged_reason
> -fieldsplit_0_mg_levels_ksp_monitor_true_residual
> -fieldsplit_0_mg_levels_ksp_converged_reason
> -fieldsplit_1_ksp_monitor_true_residual -fieldsplit_1_ksp_converged_reason
>
> and all the error output.
>
> Thanks,
>
> Matt
>
>
>> Thanks,
>>
>> Xiaofeng
>>
>>
>> On Jun 12, 2025, at 20:50, Mark Adams <mfadams at lbl.gov> wrote:
>>
>>
>>
>> On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>>> On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <mfadams at lbl.gov> wrote:
>>>
>>>> Adding this to the PETSc mailing list,
>>>>
>>>> On Thu, Jun 12, 2025 at 3:43 AM hexioafeng <hexiaofeng at buaa.edu.cn>
>>>> wrote:
>>>>
>>>>>
>>>>> Dear Professor,
>>>>>
>>>>> I hope this message finds you well.
>>>>>
>>>>> I am an employee at a CAE company and a heavy user of the PETSc
>>>>> library. I would like to thank you for your contributions to PETSc and
>>>>> express my deep appreciation for your work.
>>>>>
>>>>> Recently, I encountered some difficulties when using PETSc to solve
>>>>> structural mechanics problems with Lagrange multiplier constraints. After
>>>>> searching extensively online and reviewing several papers, I found your
>>>>> previous paper titled "*Algebraic multigrid methods for constrained
>>>>> linear systems with applications to contact problems in solid mechanics*"
>>>>> seems to be the most relevant and helpful.
>>>>>
>>>>> The stiffness matrix I'm working with, *K*, is a block saddle-point
>>>>> matrix of the form (A00 A01; A10 0), where *A00 is singular*—just as
>>>>> described in your paper, and different from many other articles . I have a
>>>>> few questions regarding your work and would greatly appreciate your
>>>>> insights:
>>>>>
>>>>> 1. Is the *AMG/KKT* method presented in your paper available in
>>>>> PETSc? I tried using *CG+GAMG* directly but received a
>>>>> *KSP_DIVERGED_PC_FAILED* error. I also attempted to use
>>>>> *CG+PCFIELDSPLIT* with the following options:
>>>>>
>>>>
>>>> No
>>>>
>>>>
>>>>>
>>>>> -pc_type fieldsplit -pc_fieldsplit_detect_saddle_point
>>>>> -pc_fieldsplit_type schur -pc_fieldsplit_schur_precondition selfp
>>>>> -pc_fieldsplit_schur_fact_type full -fieldsplit_0_ksp_type preonly
>>>>> -fieldsplit_0_pc_type gamg -fieldsplit_1_ksp_type preonly
>>>>> -fieldsplit_1_pc_type bjacobi
>>>>>
>>>>> Unfortunately, this also resulted in a *KSP_DIVERGED_PC_FAILED* error.
>>>>> Do you have any suggestions?
>>>>>
>>>>> 2. In your paper, you compare the method with *Uzawa*-type
>>>>> approaches. To my understanding, Uzawa methods typically require A00 to be
>>>>> invertible. How did you handle the singularity of A00 to construct an
>>>>> M-matrix that is invertible?
>>>>>
>>>>>
>>>> You add a regularization term like A01 * A10 (like springs). See the
>>>> paper or any reference to augmented lagrange or Uzawa
>>>>
>>>>
>>>> 3. Can i implement the AMG/KKT method in your paper using existing *AMG
>>>>> APIs*? Implementing a production-level AMG solver from scratch would
>>>>> be quite challenging for me, so I’m hoping to utilize existing AMG
>>>>> interfaces within PETSc or other packages.
>>>>>
>>>>>
>>>> You can do Uzawa and make the regularization matrix with matrix-matrix
>>>> products. Just use AMG for the A00 block.
>>>>
>>>>
>>>>
>>>>> 4. For saddle-point systems where A00 is singular, can you recommend
>>>>> any more robust or efficient solutions? Alternatively, are you aware of any
>>>>> open-source software packages that can handle such cases out-of-the-box?
>>>>>
>>>>>
>>>> No, and I don't think PETSc can do this out-of-the-box, but others may
>>>> be able to give you a better idea of what PETSc can do.
>>>> I think PETSc can do Uzawa or other similar algorithms but it will not
>>>> do the regularization automatically (it is a bit more complicated than just
>>>> A01 * A10)
>>>>
>>>
>>> One other trick you can use is to have
>>>
>>> -fieldsplit_0_mg_coarse_pc_type svd
>>>
>>> This will use SVD on the coarse grid of GAMG, which can handle the null
>>> space in A00 as long as the prolongation does not put it back in. I have
>>> used this for the Laplacian with Neumann conditions and for freely floating
>>> elastic problems.
>>>
>>>
>> Good point.
>> You can also use -pc_gamg_parallel_coarse_grid_solver to get GAMG to use
>> a on level iterative solver for the coarse grid.
>>
>>
>>> Thanks,
>>>
>>> Matt
>>>
>>>
>>>> Thanks,
>>>> Mark
>>>>
>>>>>
>>>>> Thank you very much for taking the time to read my email. Looking
>>>>> forward to hearing from you.
>>>>>
>>>>>
>>>>>
>>>>> Sincerely,
>>>>>
>>>>> Xiaofeng He
>>>>> -----------------------------------------------------
>>>>>
>>>>> Research Engineer
>>>>>
>>>>> Internet Based Engineering, Beijing, China
>>>>>
>>>>>
>>>
>>> --
>>> 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!dYETsi-moODALE1tmLrk5pxFKF9l552nNiC0cBgsCQ9ebugJWHtsNYa0QBS5Gmws9J_VC_Iec3Nx0Rvlk5er$
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>>>
>>
>>
>
> --
> 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!dYETsi-moODALE1tmLrk5pxFKF9l552nNiC0cBgsCQ9ebugJWHtsNYa0QBS5Gmws9J_VC_Iec3Nx0Rvlk5er$
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>
>
>
>
--
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!dYETsi-moODALE1tmLrk5pxFKF9l552nNiC0cBgsCQ9ebugJWHtsNYa0QBS5Gmws9J_VC_Iec3Nx0Rvlk5er$ <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!dYETsi-moODALE1tmLrk5pxFKF9l552nNiC0cBgsCQ9ebugJWHtsNYa0QBS5Gmws9J_VC_Iec3Nx0c1FgNl1$ >
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