[petsc-users] Questions Regarding PETSc and Solving Constrained Structural Mechanics Problems

Fri Jun 13 08:09:44 CDT 2025

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!f-YJSzthRa7atIa1xs1GPHW53hGIqSenvp1eO2kDsSyf4jv1_Vp0kL9Lg8pyyPeG8al4Im8XlLqGRJrGY1qm$ 
>> <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

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