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

Barry Smith bsmith at petsc.dev
Fri Jun 13 18:28:57 CDT 2025 

  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 <mailto: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 <mailto:mfadams at lbl.gov>> wrote:
>>> 
>>> 
>>> 
>>> On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
>>>> On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <mfadams at lbl.gov <mailto: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 <mailto: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!ZuoxH7bPBC1jOgKxEkOzrXMRMf5S0R1zN2saKcW7TzoFI_OEmGiIFpgThYwQTcRZl5Jng_QkCfFT_HbMDqES5mI$  <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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