[petsc-users] What is the right way to implement a (block) Diagonal ILU as PC?
Smith, Barry F.
bsmith at mcs.anl.gov
Wed Feb 5 15:42:04 CST 2020
> On Feb 5, 2020, at 4:36 AM, Hao DONG <dong-hao at outlook.com> wrote:
>
> Thanks a lot for your suggestions, Hong and Barry -
>
> As you suggested, I first tried the LU direct solvers (built-in and MUMPs) out this morning, which work perfectly, albeit slow. As my problem itself is a part of a PDE based optimization, the exact solution in the searching procedure is not necessary (I often set a relative tolerance of 1E-7/1E-8, etc. for Krylov subspace methods). Also tried BJACOBI with exact LU, the KSP just converges in one or two iterations, as expected.
>
> I added -kspview option for the D-ILU test (still with Block Jacobi as preconditioner and bcgs as KSP solver). The KSPview output from one of the examples in a toy model looks like:
>
> KSP Object: 1 MPI processes
> type: bcgs
> maximum iterations=120, nonzero initial guess
> tolerances: relative=1e-07, absolute=1e-50, divergence=10000.
> left preconditioning
> using PRECONDITIONED norm type for convergence test
> PC Object: 1 MPI processes
> type: bjacobi
> number of blocks = 3
> Local solve is same for all blocks, in the following KSP and PC objects:
> KSP Object: (sub_) 1 MPI processes
> type: preonly
> maximum iterations=10000, initial guess is zero
> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
> left preconditioning
> using NONE norm type for convergence test
> PC Object: (sub_) 1 MPI processes
> type: ilu
> out-of-place factorization
> 0 levels of fill
> tolerance for zero pivot 2.22045e-14
> matrix ordering: natural
> factor fill ratio given 1., needed 1.
> Factored matrix follows:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=11294, cols=11294
> package used to perform factorization: petsc
> total: nonzeros=76008, allocated nonzeros=76008
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: seqaij
> rows=11294, cols=11294
> total: nonzeros=76008, allocated nonzeros=76008
> total number of mallocs used during MatSetValues calls=0
> not using I-node routines
> linear system matrix = precond matrix:
> Mat Object: 1 MPI processes
> type: mpiaij
> rows=33880, cols=33880
> total: nonzeros=436968, allocated nonzeros=436968
> total number of mallocs used during MatSetValues calls=0
> not using I-node (on process 0) routines
>
> do you see something wrong with my setup?
>
> I also tried a quick performance test with a small 278906 by 278906 matrix (3850990 nnz) with the following parameters:
>
> -ksp_type bcgs -pc_type bjacobi -pc_bjacobi_local_blocks 3 -pc_sub_type ilu -ksp_view
>
> Reducing the relative residual to 1E-7
>
> Took 4.08s with 41 bcgs iterations.
>
> Merely changing the -pc_bjacobi_local_blocks to 6
>
> Took 7.02s with 73 bcgs iterations. 9 blocks would further take 9.45s with 101 bcgs iterations.
This is normal. more blocks slower convergence
>
> As a reference, my home-brew Fortran code solves the same problem (3-block D-ILU0) in
>
> 1.84s with 24 bcgs iterations (the bcgs code is also a home-brew one)…
>
Run the PETSc code with optimization ./configure --with-debugging=0 an run the code with -log_view this will show where the PETSc code is spending the time (send it to use)
>
>
> Well, by saying “use explicit L/U matrix as preconditioner”, I wonder if a user is allowed to provide his own (separate) L and U Mat for preconditioning (like how it works in Matlab solvers), e.g.
>
> x = qmr(A,b,Tol,MaxIter,L,U,x)
>
> As I already explicitly constructed the L and U matrices in Fortran, it is not hard to convert them to Mat in Petsc to test Petsc and my Fortran code head-to-head. In that case, the A, b, x, and L/U are all identical, it would be easier to see where the problem came from.
>
>
No, we don't provide this kind of support
>
> BTW, there is another thing I wondered - is there a way to output residual in unpreconditioned norm? I tried to
>
> call KSPSetNormType(ksp_local, KSP_NORM_UNPRECONDITIONED, ierr)
>
> But always get an error that current ksp does not support unpreconditioned in LEFT/RIGHT (either way). Is it possible to do that (output unpreconditioned residual) in PETSc at all?
-ksp_monitor_true_residual You can also run GMRES (and some other methods) with right preconditioning, -ksp_pc_side right then the residual computed is by the algorithm the unpreconditioned residual
KSPSetNormType sets the norm used in the algorithm, it generally always has to left or right, only a couple algorithms support unpreconditioned directly.
Barry
>
> Cheers,
> Hao
>
>
> From: Smith, Barry F. <bsmith at mcs.anl.gov>
> Sent: Tuesday, February 4, 2020 8:27 PM
> To: Hao DONG <dong-hao at outlook.com>
> Cc: petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> Subject: Re: [petsc-users] What is the right way to implement a (block) Diagonal ILU as PC?
>
>
>
> > On Feb 4, 2020, at 12:41 PM, Hao DONG <dong-hao at outlook.com> wrote:
> >
> > Dear all,
> >
> >
> > I have a few questions about the implementation of diagonal ILU PC in PETSc. I want to solve a very simple system with KSP (in parallel), the nature of the system (finite difference time-harmonic Maxwell) is probably not important to the question itself. Long story short, I just need to solve a set of equations of Ax = b with a block diagonal system matrix, like (not sure if the mono font works):
> >
> > |X |
> > A =| Y |
> > | Z|
> >
> > Note that A is not really block-diagonal, it’s just a multi-diagonal matrix determined by the FD mesh, where most elements are close to diagonal. So instead of a full ILU decomposition, a D-ILU is a good approximation as a preconditioner, and the number of blocks should not matter too much:
> >
> > |Lx | |Ux |
> > L = | Ly | and U = | Uy |
> > | Lz| | Uz|
> >
> > Where [Lx, Ux] = ILU0(X), etc. Indeed, the D-ILU preconditioner (with 3N blocks) is quite efficient with Krylov subspace methods like BiCGstab or QMR in my sequential Fortran/Matlab code.
> >
> > So like most users, I am looking for a parallel implement with this problem in PETSc. After looking through the manual, it seems that the most straightforward way to do it is through PCBJACOBI. Not sure I understand it right, I just setup a 3-block PCJACOBI and give each of the block a KSP with PCILU. Is this supposed to be equivalent to my D-ILU preconditioner? My little block of fortran code would look like:
> > ...
> > call PCBJacobiSetTotalBlocks(pc_local,Ntotal, &
> > & isubs,ierr)
> > call PCBJacobiSetLocalBlocks(pc_local, Nsub, &
> > & isubs(istart:iend),ierr)
> > ! set up the block jacobi structure
> > call KSPSetup(ksp_local,ierr)
> > ! allocate sub ksps
> > allocate(ksp_sub(Nsub))
> > call PCBJacobiGetSubKSP(pc_local,Nsub,istart, &
> > & ksp_sub,ierr)
> > do i=1,Nsub
> > call KSPGetPC(ksp_sub(i),pc_sub,ierr)
> > !ILU preconditioner
> > call PCSetType(pc_sub,ptype,ierr)
> > call PCFactorSetLevels(pc_sub,1,ierr) ! use ILU(1) here
> > call KSPSetType(ksp_sub(i),KSPPREONLY,ierr)]
> > end do
> > call KSPSetTolerances(ksp_local,KSSiter%tol,PETSC_DEFAULT_REAL, &
> > & PETSC_DEFAULT_REAL,KSSiter%maxit,ierr)
> > …
>
> This code looks essentially right. You should call with -ksp_view to see exactly what PETSc is using for a solver.
>
> >
> > I understand that the parallel performance may not be comparable, so I first set up a one-process test (with MPIAij, but all the rows are local since there is only one process). The system is solved without any problem (identical results within error). But the performance is actually a lot worse (code built without debugging flags in performance tests) than my own home-brew implementation in Fortran (I wrote my own ILU0 in CSR sparse matrix format), which is hard to believe. I suspect the difference is from the PC as the PETSc version took much more BiCGstab iterations (60-ish vs 100-ish) to converge to the same relative tol.
>
> PETSc uses GMRES by default with a restart of 30 and left preconditioning. It could be different exact choices in the solver (which is why -ksp_view is so useful) can explain the differences in the runs between your code and PETSc's
> >
> > This is further confirmed when I change the setup of D-ILU (using 6 or 9 blocks instead of 3). While my Fortran/Matlab codes see minimal performance difference (<5%) when I play with the D-ILU setup, increasing the number of D-ILU blocks from 3 to 9 caused the ksp setup with PCBJACOBI to suffer a performance decrease of more than 50% in sequential test.
>
> This is odd, the more blocks the smaller each block so the quicker the ILU set up should be. You can run various cases with -log_view and send us the output to see what is happening at each part of the computation in time.
>
> > So my implementation IS somewhat different in PETSc. Do I miss something in the PCBJACOBI setup? Or do I have some fundamental misunderstanding of how PCBJACOBI works in PETSc?
>
> Probably not.
> >
> > If this is not the right way to implement a block diagonal ILU as (parallel) PC, please kindly point me to the right direction. I searched through the mail list to find some answers, only to find a couple of similar questions... An example would be nice.
>
> You approach seems fundamentally right but I cannot be sure of possible bugs.
> >
> > On the other hand, does PETSc support a simple way to use explicit L/U matrix as a preconditioner? I can import the D-ILU matrix (I already converted my A matrix into Mat) constructed in my Fortran code to make a better comparison. Or do I have to construct my own PC using PCshell? If so, is there a good tutorial/example to learn about how to use PCSHELL (in a more advanced sense, like how to setup pc side and transpose)?
>
> Not sure what you mean by explicit L/U matrix as a preconditioner. As Hong said, yes you can use a parallel LU from MUMPS or SuperLU_DIST or Pastix as the solver. You do not need any shell code. You simply need to set the PCType to lu
>
> You can also set all this options from the command line and don't need to write the code specifically. So call KSPSetFromOptions() and then for example
>
> -pc_type bjacobi -pc_bjacobi_local_blocks 3 -pc_sub_type ilu (this last one is applied to each block so you could use -pc_type lu and it would use lu on each block.)
>
> -ksp_type_none -pc_type lu -pc_factor_mat_solver_type mumps (do parallel LU with mumps)
>
> By not hardwiring in the code and just using options you can test out different cases much quicker
>
> Use -ksp_view to make sure that is using the solver the way you expect.
>
> Barry
>
>
>
> Barry
>
> >
> > Thanks in advance,
> >
> > Hao
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