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

[hexioafeng]

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.

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 <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
>> 
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