Thank you very much Pierre! I was not aware of the fact that the fill-in in the ILU decides about its quality. But its clear now. I will just test what level of fill we need for our application.
Once more thanks, Nils Pierre Jolivet <[email protected]> writes: >> On 24 Oct 2025, at 1:52 PM, Nils Schween <[email protected]> wrote: >> >> Dear PETSc users, Dear PETSc developers, >> >> in our software we are solving a linear system with PETSc using GMRES >> in conjunction with a BlockJacobi preconditioner, i.e. the default of >> the KSP object. >> >> We have two versions of the system matrix, say A and B. The difference >> between them is the non-zero pattern. The non-zero pattern of matrix B >> is a subset of the one of matrix A. Their values should be identical. >> >> We solve the linear system, using A yields a solution after some >> iterations, whereas using B does not converge. >> >> I created binary files of the two matrices, the right-hand side, and >> wrote a small PETSc programm, which loads them and demonstrates the >> issue. I attach the files to this email. >> >> We would like to understand why the solver-preconditioner combination >> works in case A and not in case B. Can you help us finding this out? >> >> To test if the two matrices are identical, I substracted them and >> computed the Frobenius norm of the result. It is zero. > > The default subdomain solver is ILU(0). > By definition, this won’t allow fill-in. > So when you are not storing the zeros in B, the quality of your PC is much > worse. > You can check this yourself with -A_ksp_view -B_ksp_view: > […] > 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: (A_) 1 MPI process > type: seqaij > rows=1664, cols=1664 > package used to perform factorization: petsc > total: nonzeros=117760, allocated nonzeros=117760 > using I-node routines: found 416 nodes, limit used is 5 > […] > 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: (B_) 1 MPI process > type: seqaij > rows=1664, cols=1664 > package used to perform factorization: petsc > total: nonzeros=49408, allocated nonzeros=49408 > not using I-node routines > > Check the number of nonzeros of both factored Mat. > With -B_pc_factor_levels 3, you’ll get roughly similar convergence speed (and > density in the factored Mat of both PC). > > Thanks, > Pierre > >> >> To give you more context, we solve a system of partial differential >> equations that models astrophysical plasmas. It is essentially a system >> of advection-reaction equations. We use a discontinuous Galerkin (dG) >> method. Our code relies on the finite element library library deal.ii >> and its PETSc interface. The system matrices A and B are the result of >> the (dG) discretisation. We GMRES with a BlockJaboci preconditioner, >> because we do not know any better. >> >> I tested the code I sent with PETSc 3.24.0 and 3.19.1 on my workstation, i.e. >> Linux home-desktop 6.17.2-arch1-1 #1 SMP PREEMPT_DYNAMIC Sun, 12 Oct 2025 >> 12:45:18 +0000 x86_64 GNU/Linux >> I use OpenMPI 5.0.8 and I compiled with mpicc, which in my cases use >> gcc. >> >> In case you need more information. Please let me know. >> Any help is appreciated. >> >> Thank you, >> Nils >> <example.tar.gz> >> >> -- >> Nils Schween >> >> Phone: +49 6221 516 557 >> Mail: [email protected] >> PGP-Key: 4DD3DCC0532EE96DB0C1F8B5368DBFA14CB81849 >> >> Max Planck Institute for Nuclear Physics >> Astrophysical Plasma Theory (APT) >> Saupfercheckweg 1, D-69117 Heidelberg >> https://www.mpi-hd.mpg.de/mpi/en/research/scientific-divisions-and-groups/independent-research-groups/apt -- Nils Schween PhD Student Phone: +49 6221 516 557 Mail: [email protected] PGP-Key: 4DD3DCC0532EE96DB0C1F8B5368DBFA14CB81849 Max Planck Institute for Nuclear Physics Astrophysical Plasma Theory (APT) Saupfercheckweg 1, D-69117 Heidelberg https://www.mpi-hd.mpg.de/mpi/en/research/scientific-divisions-and-groups/independent-research-groups/apt
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