[petsc-users] Sparse linear system solving

Matthew Knepley knepley at gmail.com
Mon May 30 21:17:45 CDT 2022

On Mon, May 30, 2022 at 10:12 PM Lidia <lidia.varsh at mail.ioffe.ru> wrote:

> Dear colleagues,
> Is here anyone who have solved big sparse linear matrices using PETSC?

There are lots of publications with this kind of data. Here is one recent
one: https://arxiv.org/abs/2204.01722

> We have found NO performance improvement while using more and more mpi
> processes (1-2-3) and open-mp threads (from 1 to 72 threads). Did anyone
> faced to this problem? Does anyone know any possible reasons of such
> behaviour?

Solver behavior is dependent on the input matrix. The only general-purpose
are direct, but they do not scale linearly and have high memory

Thus, in order to make progress you will have to be specific about your

> We use AMG preconditioner and GMRES solver from KSP package, as our
> matrix is large (from 100 000 to 1e+6 rows and columns), sparse,
> non-symmetric and includes both positive and negative values. But
> performance problems also exist while using CG solvers with symmetric
> matrices.

There are many PETSc examples, such as example 5 for the Laplacian, that
good scaling with both AMG and GMG.

> Could anyone help us to set appropriate options of the preconditioner
> and solver? Now we use default parameters, maybe they are not the best,
> but we do not know a good combination. Or maybe you could suggest any
> other pairs of preconditioner+solver for such tasks?
> I can provide more information: the matrices that we solve, c++ script
> to run solving using petsc and any statistics obtained by our runs.

First, please provide a description of the linear system, and the output of

  -ksp_view -ksp_monitor_true_residual -ksp_converged_reason -log_view

for each test case.



> Thank you in advance!
> Best regards,
> Lidiia Varshavchik,
> Ioffe Institute, St. Petersburg, Russia

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://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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