I am trying to apply a user-defined preconditioner to speed up the convergency of matrix-free KSP solver. The user's manual provides an example of how to call the user-defined preconditioner routine. The routine has PC, input Vec and output Vec as arguments. I want to use part of the Jacobian as preconditioner matrix, the elements of which can be calculated using input Vec. My question is what the role of output Vec from the routine is in matrix-vector product? Or I just have the preconditioner matrix elements calculated in the routine and then Petsc handles applying the preconditioner to matrix-vector product? I used PCSetType(pc, PCSHELL) and PCShellSetApply.
Thank you and appreciate your help! Jiannan ________________________________ From: Tu, Jiannan <jiannan...@uml.edu> Sent: Wednesday, July 6, 2022 2:34 PM To: Barry Smith <bsm...@petsc.dev> Cc: Jed Brown <j...@jedbrown.org>; petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov> Subject: Re: [petsc-users] Using matrix-free with KSP Barry, VecScatterCreateToAll solves the problem! The code now gives the correct answer with multiple processes. Thank you all so much! Jiannan ________________________________ From: Barry Smith <bsm...@petsc.dev> Sent: Wednesday, July 6, 2022 2:08 PM To: Tu, Jiannan <jiannan...@uml.edu> Cc: Jed Brown <j...@jedbrown.org>; petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov> Subject: Re: [petsc-users] Using matrix-free with KSP So your operator is a "dense" operator in that its matrix representation would be essentially dense. In that case, you can use specialized routines to do this efficiently. You can use VecScatterCreateToAll() and then VecScatterBegin/End to do the communication. Barry On Jul 6, 2022, at 1:39 PM, Tu, Jiannan <jiannan...@uml.edu<mailto:jiannan...@uml.edu>> wrote: Jed, thank you very much for the reply. I'm not sure GlobaltoLocal will work. Say the solution vector is of length 10. Two processes then each process can see 5 elements of the vector. For A x = b (10 equations), each process performs matrix-vector product for five equations. And for each equation i , sum_j A_ij * x_j = b_i requires the process has access to all 10 unknows x_i (i=0,1,...,9). Can VecScatter and PetscSF make the entire vector accessible to each process? I am reading the manual and trying to understand how VecScatter and PetscSF work. Jiannan ________________________________ From: Jed Brown <j...@jedbrown.org<mailto:j...@jedbrown.org>> Sent: Wednesday, July 6, 2022 10:09 AM To: Tu, Jiannan <jiannan...@uml.edu<mailto:jiannan...@uml.edu>>; Barry Smith <bsm...@petsc.dev<mailto:bsm...@petsc.dev>> Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov> <petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>> Subject: Re: [petsc-users] Using matrix-free with KSP You'll usually have a GlobalToLocal operation for each rank to get the halo data it needs, then either a LocalToGlobal to collect the result (e.g., finite element methods) or the local compute will write directly into the owned portion of the global vector. If you're doing the communication "raw", then you may find VecScatter or PetscSF useful to perform the necessary communication. "Tu, Jiannan" <jiannan...@uml.edu<mailto:jiannan...@uml.edu>> writes: > Hi Barry, > > Following your instructions I implemented the matrix-free method to solve a > large linear equation system resulted from a surface integration equation. > The KSP solver works fine for single process, but it is problematic with > multiple processes. The problem is that each process only can access its own > part of solution vector so that each process only conducts part of > matrix-vector multiplication. MPI can be used to assemble these partial > matrix-vector multiplication together. Does Petsc provide any ways to > implement multi-process matrix-free method? > > Thanks, > Jiannan > ________________________________ > From: Barry Smith <bsm...@petsc.dev<mailto:bsm...@petsc.dev>> > Sent: Tuesday, May 24, 2022 2:12 PM > To: Tu, Jiannan <jiannan...@uml.edu<mailto:jiannan...@uml.edu>> > Cc: petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov> > <petsc-users@mcs.anl.gov<mailto:petsc-users@mcs.anl.gov>> > Subject: Re: [petsc-users] Using matrix-free with KSP > > This e-mail originated from outside the UMass Lowell network. > ________________________________ > > You can use MatCreateMFFD > https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FMat%2FMatCreateMFFD%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7Cab0859d8d154471590bc08da5f5918d6%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637927133525745809%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=A7wqegTfh94No5BpDiWLK3VxOuR44U2wlWHVm2k7l60%3D&reserved=0<https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/Mat/MatCreateMFFD/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d10-zlXkw$><https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FMat%2FMatCreateMFFD%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C60675432e0b5409f004908da5f7a8b29%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637927277198462552%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=7SEmNO9TybDxwnhwcmyW1vFVc2eo7ys8JGBv9%2F%2FR2eI%3D&reserved=0> > MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix > to KSP. Note you will need to use -pc_type none or provide your own custom > preconditioner > withhttps://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FPC%2FPCSHELL%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7Cab0859d8d154471590bc08da5f5918d6%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637927133525745809%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=Gb%2F9uFG3jp%2FbfWaSh2cSEQLItHS9CuLwarzN0KcNiJY%3D&reserved=0<https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/PC/PCSHELL/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d1cA4fKGw$><https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FPC%2FPCSHELL%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C60675432e0b5409f004908da5f7a8b29%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637927277198462552%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=FDGqXk2UbO%2FYef5n21SIAUYrte093iKgL2p%2FwoA3qec%3D&reserved=0> > > > > On May 24, 2022, at 1:21 PM, Tu, Jiannan > <jiannan...@uml.edu<mailto:jiannan...@uml.edu><mailto:jiannan...@uml.edu>> > wrote: > > I want to use a matrix-free matrix to solve a large linear equation system > because the matrix is too large to be stored. Petsc user manual describes > matrix-free method for SNES with examples. The matrix-free matrices section > explains how to set up such a matrix, but I can't find any example of > matrix-free method with KSP. I am wondering how to apply the method to KSP > iterative solver in parallel. > > I greatly appreciate your help for me to understand this topic. > > Jiannan Tu
