[petsc-users] Using matrix-free with KSP
Tu, Jiannan
Jiannan_Tu at uml.edu
Mon Aug 22 11:25:04 CDT 2022
The matrix-vector product involves part of matrix elements explicitly as shown below so that I need to insert values into this part of the matrix.
[cid:07fd6bc2-973b-4485-8416-e22ba5302a62]
Initially I wrote my own code for calculating and storing matrix A^near_mi without using any Petsc matrix and then performed matrix-vector product using above equation. The code runs but converges very slow. Apparently a preconditioned is needed.
I am not clear how Petsc can provide a preconditioner for my case.
________________________________
From: Barry Smith <bsmith at petsc.dev>
Sent: Monday, August 22, 2022 8:42 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu>
Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
On Aug 21, 2022, at 11:18 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Barry,
You are right. With PC type none, the same error appears.
Now I use MatShell and I literally have three matrixes. A is a shell matrix, B is a preconditioner, and C is a matrix just for preallocation purpose.
First C is used to determine non-zero structure. Then use MatPreallocatorPreallocation(C, PETSC_FALSE, B) to preallocate for B. After that do insertion and assembly for B. These steps work fine.
Now the question is how to insert and assemble shell matrix A. MatPreallocatorPreallocation doesn’t work with shell matrix as indicated by an error message. MatSetValues or Mat assembly doesn’t support shell matrix either.
A shell matrix is completely under your control. You decide on what data you want to store in it, and you provide the matrix-vector product routine. MatPreallocatorPreallocation and MatSetValues don't work for shell matrix unless you provide code for them to work, which normally you would not do.
I don't understand why you want to use MatSetValues for your shell matrix. If you can use MatSetValues() and just build an explicit matrix, then why would you use a shell matrix, just use MATAIJ matrix?
Or does part of the operation inside your MatShell require a "regular" PETSc matrix? This would be fine, but it is your responsibility to design your Mat shell context to contain the "regular matrix" and your responsibility to fill up that regular matrix inside your shell context, calling whatever code you choose to write. So for example your shell context would be a C struct and one of the fields would be a regular PETSc matrix, also part of your custom matrix-vector product routine would call a regular MatMult() on the regular PETSc matrix stored inside the C struct.
Barry
Thank you,
Jiannan
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Friday, August 19, 2022 4:02 PM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
I don't know why changing the PCType could matter, can you please try with your new code but use the -pc_type none option to turn off the use of the preconditioner to see if the error still appears (I think it should).
Also if you have a custom function that can do the matrix-vector product (not using any differencing) then you should use MatShell() and provide the matrix-vector product operation with your code.
Barry
On Aug 19, 2022, at 11:47 AM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Barry,
I have my own matrix-vector product but not use MatShell. I followed your previous instruction to use
MatCreateMFFD(MPI_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, N, N, &A);
MatMFFDSetFunction(A, formfunction, ¶ms);
MatSetFromOptions(A);
MatMFFDSetBase(A, X, NULL);
The customized matrix-vector product is implemented in formfunction() provided to MatMFFDSetFunction(). In this way, the matrix A is not used. I think that is why Petsc complains the matrix is not assembled. However, when PC type is none, the code runs without error although KSP solver doesn’t converge.
The question then becomes how to link A to matrix-free matrix-vector multiplication. And where to put MatShell?
Thank you,
Jiannan
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Friday, August 19, 2022 10:27 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
On Aug 18, 2022, at 11:41 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
The program calls KSPSolve just once and the error occurs after the first iteration.
I realized the matrix-vector product in my case is different from that approximating matrix-vector multiply by finite difference of function vector. It consists of two parts. One is multiplication of part of the matrix with part of vector, and another part results from so called fast multipole method. I’m not clear how to relate such calculation of matrix-vector product to the finite differencing of function vector.
Are you using finite differencing at all in a matrix-vector product, or do you have your own custom matrix-vector product code (with MatShell)?
Anyways the easiest thing to do is
use the run time option -on_error_attach_debugger noxterm and run the code,
when it stops in the debugger you can type bt (for backtrace)
then do up a few times to move up the stack until you get to the PETSc function call that generates the error
you can then do "call MatView(thematrixvarible,0) to have PETSc display what the matrix is and
you can also do print *thematrixvariable to see the exact struct with all its fields
If this doesn't tell you why the troublesome matrix is not assembled then cut and paste ALL of the output and email it
Barry
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Thursday, August 18, 2022 7:44 PM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
Is it in the first iteration of the first KSPSolve that you get this message? Or in the second call to KSPSolve?
The error comes from a matrix vector product with your A matrix, what is that and where did it come from. The error message is not from your B matrix, that is not used in the MatMult()
On Aug 18, 2022, at 3:05 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Barry,
Thanks. The method works. Assembly of actual matrix now completes quickly. The convergency is much better for the first iteration. The residual normal is in the order of 10^-10 instead of 10^-2. However, there is an error message after the first iteration: “Object is in wrong state. Not for unassembled matrix” even though both preallocator and actual matrix have been assembled (see the code snippet below). Could you please give me some hints what’s going wrong? I use KSP type bcgs and PC type mat
Thank you,
Jiannan
-----------------------------------------------------
Solve linear equations ...
0 KSP Residual norm 9.841179147519e-10
[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
[0]PETSC ERROR: Object is in wrong state
[0]PETSC ERROR: Not for unassembled matrix
[0]PETSC ERROR: See https://petsc.org/release/faq/<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Ffaq%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=yku5%2F0k1g7PMAwuI4WGQ5MmM4g7OUh0C9EvjaWAJAAE%3D&reserved=0> for trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022
[0]PETSC ERROR: ./iesolver on a named REXNET-WS4 by jiannantu Thu Aug 18 14:48:43 2022
[0]PETSC ERROR: Configure options --download-f2cblaslapack=yes --with-mpi-dir=/usr/local --with-fc=0 --prefix=/home/jiannantu/petsc --with-scalar-type=complex --with-64-bit-indices=1
[0]PETSC ERROR: #1 MatMult() at /home/jiannantu/petsc-3.16.6/src/mat/interface/matrix.c:2425
[0]PETSC ERROR: #2 PCApplyBAorAB() at /home/jiannantu/petsc-3.16.6/src/ksp/pc/interface/precon.c:730
[0]PETSC ERROR: #3 KSP_PCApplyBAorAB() at /home/jiannantu/petsc-3.16.6/include/petsc/private/kspimpl.h:421
[0]PETSC ERROR: Linear equations not solved. Diverged reason: 0
#4 KSPSolve_BCGS() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/impls/bcgs/bcgs.c:87
[0]PETSC ERROR: #5 KSPSolve_Private() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/interface/itfunc.c:914
[0]PETSC ERROR: #6 KSPSolve() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/interface/itfunc.c:1086
-----------------------------------------------
MatCreate(MPI_COMM_WORLD, &B);
MatSetType(B, MATMPIAIJ);
MatSetSizes(B, PETSC_DECIDE, PETSC_DECIDE, N, N);
Mat preall;
MatCreate(MPI_COMM_WORLD, &preall);
MatSetType(preall, MATPREALLOCATOR);
MatSetSizes(preall, PETSC_DECIDE, PETSC_DECIDE, N, N);
MatMPIAIJSetPreallocation(preall, 0, d_nnz, 0, o_nnz);
MatSetUp(preall);
MatSetOption(preall, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
//set values row by row
MatSetValues(preall, 1, &m, 1, nCols, matCols, INSERT_VALUES);
MatAssemblyBegin(preall, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(preall, MAT_FINAL_ASSEMBLY);
//set values for actual matrix row by row
MatSetValues(B, 1, &m, 1, nCols, matCols, INSERT_VALUES);
MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
KSPCreate(MPI_COMM_WORLD, &ksp);
KSPSetOperators(ksp, A, B);
KSPSetFromOptions(ksp);
PC pc;
KSPGetPC(ksp, &pc);
PCSetFromOptions(pc);
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Thursday, August 18, 2022 12:59 PM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
Yes, once you have preallocated the real matrix you can destroy the preallocation matrix whose only job is to gather the preallocation information
On Aug 18, 2022, at 12:52 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Thanks, Barry.
So I need actually two matrixes, one for preallocator and one for actual matrix that can be passed to KSPSetOperators(). -mat_type preallocator option is used to speed up doing insertion into preallocator, then use MatPreallocatorPreallocate() to preallocate actual matrix and do actual insertion of values into it., right?
The code runs in parallel. Each process owns number of rows that equals to number of unknowns (that is, xm in 1D DM) it owns.
Jiannan
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Thursday, August 18, 2022 11:37 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
The preallocator MatType matrix cannot be passed to the KSPSetOperators(), you need to create an actual matrix, for example MATAIJ and use the preallocator to set its preallocation and then fill up the MATAIJ matrix with the usual MatSetValues and pass that matrix to the KSPSetOperators.
On Aug 18, 2022, at 11:30 AM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Hi Barry,
The MATPREALLOCATOR solved problem of slow matrix assembly. But the solver failed because of “Matrix type preallocator does not have a multiply defined”.
I guess this is because the matrix-free is used. I am wondering how a preconditioner is applied to the matrix-vector multiply in Petsc.
Thank you,
Jiannan
[0]PETSC ERROR: No support for this operation for this object type
[0]PETSC ERROR: Matrix type preallocator does not have a multiply defined
[0]PETSC ERROR: See https://petsc.org/release/faq/<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Frelease%2Ffaq%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=yku5%2F0k1g7PMAwuI4WGQ5MmM4g7OUh0C9EvjaWAJAAE%3D&reserved=0> for trouble shooting.
[0]PETSC ERROR: Petsc Release Version 3.16.6, Mar 30, 2022
[0]PETSC ERROR: ./iesolver on a named REXNET-WS4 by jiannantu Thu Aug 18 11:21:55 2022
[0]PETSC ERROR: Configure options --download-f2cblaslapack=yes --with-mpi-dir=/usr/local --with-fc=0 --prefix=/home/jiannantu/petsc --with-scalar-type=complex --with-64-bit-indices=1
[0]PETSC ERROR: #1 MatMult() at /home/jiannantu/petsc-3.16.6/src/mat/interface/matrix.c:2437
[0]PETSC ERROR: #2 PCApply_Mat() at /home/jiannantu/petsc-3.16.6/src/ksp/pc/impls/mat/pcmat.c:9
[0]PETSC ERROR: #3 PCApply() at /home/jiannantu/petsc-3.16.6/src/ksp/pc/interface/precon.c:445
[0]PETSC ERROR: #4 KSP_PCApply() at /home/jiannantu/petsc-3.16.6/include/petsc/private/kspimpl.h:382
[0]PETSC ERROR: #5 KSPInitialResidual() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/interface/itres.c:65
[0]PETSC ERROR: #6 KSPSolve_BCGS() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/impls/bcgs/bcgs.c:43
[0]PETSC ERROR: #7 KSPSolve_Private() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/interface/itfunc.c:914
[0]PETSC ERROR: #8 KSPSolve() at /home/jiannantu/petsc-3.16.6/src/ksp/ksp/interface/itfunc.c:1086
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Thursday, August 18, 2022 8:35 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
Slow assembly is usually due to under preallocation. You can change to using
MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE);
to detect if you are under preallocating. See https://petsc.org/main/docs/manual/mat/#sec-matsparse<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanual%2Fmat%2F%23sec-matsparse&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=R%2F49HLXjwq%2FdFzTGL8mpz8X7YKi0iH0%2FWDz4FANCoD8%3D&reserved=0>. That section clearly needs some sprucing up. If it is difficult to determine good preallocation values you can use https://petsc.org/main/docs/manualpages/Mat/MATPREALLOCATOR/<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FMat%2FMATPREALLOCATOR%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=yiRv7HiBgqJxwszz%2FdV2EsO7iJ5rgVIOMeW1cyNzScI%3D&reserved=0> to compute the needed preallocation efficiently.
Are you running in parallel? If so how are you determining which rows of entries to compute on each MPI rank? You will want most of the rows to be computed on the rank where the values are stored, you can determine this with https://petsc.org/main/docs/manualpages/Mat/MatGetOwnershipRange.html<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FMat%2FMatGetOwnershipRange.html&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=W5lM%2B6UCP3%2BT5zT2uZPObqt0sZ8u841Jn79fBdikXWY%3D&reserved=0>
Barry
On Aug 18, 2022, at 12:50 AM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
I implemented the preconditioner. The solver converges quickly when the problem size is small. But when the size increases, say to 100k unknowns, the code hangs at assembly of the preconditioner matrix. The function call sequence is like this
MatCreate(MPI_COMM_WORLD, &B);
MatSetType(B, MATMPIAIJ);
MatSetSizes(B, PETSC_DECIDE, PETSC_DECIDE, N, N);
MatSetFromOptions(B);
// The number of diagonal and off diagonal non zeros only can be determined run-time.
MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz);
MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
//here insert values row by row.
MatSetValues(B, 1, &m, nn, nCols, matCols, INSERT_VALUES);
MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
Could you please tell me what I have done wrong?
Thank you,
Jiannan
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Tuesday, August 16, 2022 2:00 PM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
Create another matrix B that contains "Selected parts of the matrix can be pre-calculated and stored to serve as the preconditioner." When you call KSPSetOperators() pass in B as the second matrix argument.
Now if literally application of B is the preconditioner you want to use, then simply use PCMAT as the preconditioner, and it will apply B each time it needs to apply the preconditioner. With this, you do not even need a PCShell.
If your preconditioner uses B to construct your own specific data structure needed to apply your preconditioner, then you can use PCShellSetSetUp() and have your routine call PCGetOperators() to pull out the B matrix and use it to construct your preconditioner.
If you want PETSc to construct a standard preconditioner from B, then you don't need the PCShell; you simply pass in the B, as above, and use -pc_type type to set the preconditioner you want to use.
Barry
On Aug 16, 2022, at 12:31 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
Barry,
Thank you very much for your instructions. I am sorry I may not ask clearer questions.
I don't use SNES. What I am trying to solve is a very large linear equation system with dense and ill-conditioned matrix. Selected parts of the matrix can be pre-calculated and stored to serve as the preconditioner. My question is how I can apply this matrix as the preconditioner.
Here is the part of code from my linear equations solver. MatrixFreePreconditioner is supposed to be the routine to provide the preconditioner. But I don't understand how to use it. Should I use SNESSetJacobian() even if this is a linear problem?
MatCreateMFFD(MPI_COMM_WORLD, PETSC_DECIDE, PETSC_DECIDE, N, N, &A);
MatMFFDSetFunction(A, formfunction, ¶ms);
MatSetFromOptions(A);
MatMFFDSetBase(A, X, NULL);
KSPCreate(MPI_COMM_WORLD, &ksp);
KSPSetOperators(ksp, A, A);
KSPSetFromOptions(ksp);
PC pc;
KSPGetPC(ksp,&pc);
PCSetType(pc,PCSHELL);
PCShellSetApply(pc,MatrixFreePreconditioner);
Thank you,
Jiannan
________________________________
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Tuesday, August 16, 2022 10:10 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] Using matrix-free with KSP
CAUTION: This email was sent from outside the UMass Lowell network.
I don't fully understand your question so I will answer questions that I do know the answer to :-)
The function you provide to PCShellSetApply() applies the preconditioner to the input vector and puts the result in the output vector. This input vector changes at every application of the preconditioner so should not be used in constructing the preconditioner.
If you are using the standard PETSc matrix-free matrix-vector product via finite difference, -snes_mf_operator or via MatCreateSNESMF() or you are using a MatShell, the matrix-vector product routines input changes for each multiply and should not be used in constructing the preconditioner.
The function you provide with SNESSetJacobian() is where you can compute anything you need to help build your preconditioner. The input vector to that function is the location at which the Jacobian is needed and is what you should use to build your approximate/part of Jacobian. You can store your approximate/part of Jacobian that you need to compute in the pmat and then in a PCShellSetUp() function that you provide you will compute what you will need latter to apply the preconditioner in your PCShellSetApply() function. Note that the values you put in the pmat do not need to be the full Jacobian; they can be anything you want since this pmat is not used to apply the matrix vector product.
If this is unclear, feel free to ask additional questions.
Barry
On Aug 16, 2022, at 9:40 AM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>> wrote:
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_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Sent: Wednesday, July 6, 2022 2:34 PM
To: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Cc: Jed Brown <jed at jedbrown.org<mailto:jed at jedbrown.org>>; petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at 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 <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Wednesday, July 6, 2022 2:08 PM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
Cc: Jed Brown <jed at jedbrown.org<mailto:jed at jedbrown.org>>; petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at 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_Tu at uml.edu<mailto:Jiannan_Tu at 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 <jed at jedbrown.org<mailto:jed at jedbrown.org>>
Sent: Wednesday, July 6, 2022 10:09 AM
To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>; Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at 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_Tu at uml.edu<mailto:Jiannan_Tu at 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 <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
> Sent: Tuesday, May 24, 2022 2:12 PM
> To: Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu>>
> Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at 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$><https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FMat%2FMatCreateMFFD%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=psLU6qTaDTxSsrgXMdgpyjfdc0Pc1ZD%2BrzxDa8ThXHk%3D&reserved=0> MatMFFDSetFunction MatSetFromOptions MatMFFDSetBase and provide the matrix to KSP. Note you will need to use -pc_type none or provide your own custom preconditioner withhttps://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Fpetsc.org%2Fmain%2Fdocs%2Fmanualpages%2FPC%2FPCSHELL%2F&data=05%7C01%7CJiannan_Tu%40uml.edu%7Cab0859d8d154471590bc08da5f5918d6%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637927133525745809%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=Gb%2F9uFG3jp%2FbfWaSh2cSEQLItHS9CuLwarzN0KcNiJY%3D&reserved=0<https://urldefense.com/v3/__https://petsc.org/main/docs/manualpages/PC/PCSHELL/__;!!PVKG_VDCxu5g!stxq2NWGVjUihvHBQC9Rlk0aHVoowcy0PTQYMcQxQ4DqOEC05KSw6TmstSXKckiUgelHzy4ue-d1cA4fKGw$><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%7C76c4d9eda7804ab02ddb08da843bcb86%7C4c25b8a617f746f983f054734ab81fb1%7C0%7C0%7C637967689641631746%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=CWffbXJW4UGJifTbRNGmI2IpLYVVglfeLyzLxprZLyY%3D&reserved=0>
>
>
>
> On May 24, 2022, at 1:21 PM, Tu, Jiannan <Jiannan_Tu at uml.edu<mailto:Jiannan_Tu at uml.edu><mailto:Jiannan_Tu at 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
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