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
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 <bsm...@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 <knep...@gmail.com> wrote:
>>
>> On Thu, Jun 12, 2025 at 10:55 PM hexioafeng <hexiaof...@buaa.edu.cn
>> <mailto:hexiaof...@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 <mfad...@lbl.gov
>>>> <mailto:mfad...@lbl.gov>> wrote:
>>>>
>>>>
>>>>
>>>> On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <knep...@gmail.com
>>>> <mailto:knep...@gmail.com>> wrote:
>>>>> On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <mfad...@lbl.gov
>>>>> <mailto:mfad...@lbl.gov>> wrote:
>>>>>> Adding this to the PETSc mailing list,
>>>>>>
>>>>>> On Thu, Jun 12, 2025 at 3:43 AM hexioafeng <hexiaof...@buaa.edu.cn
>>>>>> <mailto:hexiaof...@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!e0AMQ70ZmiHfz7acc2y7bj16p9tQITJx5wjrNfKN3d2Iu_q0ghMi5CQvuisbw_fPYd8w-s_2iyDRH5xvxgTZ9JBIm5UKKQ$
>>>>>
>>>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!f-YJSzthRa7atIa1xs1GPHW53hGIqSenvp1eO2kDsSyf4jv1_Vp0kL9Lg8pyyPeG8al4Im8XlLqGRHw1FxYh$>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their experiments
>> is infinitely more interesting than any results to which their experiments
>> lead.
>> -- Norbert Wiener
>>
>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!e0AMQ70ZmiHfz7acc2y7bj16p9tQITJx5wjrNfKN3d2Iu_q0ghMi5CQvuisbw_fPYd8w-s_2iyDRH5xvxgTZ9JBIm5UKKQ$
>>
>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!f-YJSzthRa7atIa1xs1GPHW53hGIqSenvp1eO2kDsSyf4jv1_Vp0kL9Lg8pyyPeG8al4Im8XlLqGRHw1FxYh$>
>
