On Thu, Jun 12, 2025 at 8:44 AM Matthew Knepley <knep...@gmail.com> wrote:
> On Thu, Jun 12, 2025 at 4:58 AM Mark Adams <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> >> 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!cOziFPTYQhj3Q2QdRoQiCJ__wU-JwGk5zFk_C1QziJVJ9_DiXgLkG5d2QpCFzatvJgHtMFVSUfYjbKrho9pJS8A$ > > <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cOziFPTYQhj3Q2QdRoQiCJ__wU-JwGk5zFk_C1QziJVJ9_DiXgLkG5d2QpCFzatvJgHtMFVSUfYjbKrh_nneKPA$ > > >
