[petsc-users] Solver/Preconditioner suggestions

Matthew Knepley knepley at gmail.com
Thu May 19 12:30:52 CDT 2022

On Thu, May 19, 2022 at 7:27 AM Alfredo J Duarte Gomez <aduarteg at utexas.edu>

> Good afternoon PETSC users,
> I am looking for some suggestions on preconditioners/solvers.
> Currently, I have a custom preconditioner that solves 4 independent
> systems, let's call them A,B,C, and D.
> A is an advective, diffusive, reactive system, although due to some
> coefficient it is the system with the highest condition number and
> therefore the most difficult to solve.
> B and C, are more "standard" advective, diffusion, reactive systems. The
> condition number is not as high as A.
> D is simply the laplacian used to solve an elliptic Poisson equation.
> For more context, A,B, and C need to be recomputed about once every time
> step, while D is a one time cost.
> The problem is 2-D, sizes are on the order of 1-10 million grid points,
> and I am using a structured grid. These usually run on somewhere between
> 100-400 processors.
> Currently  I am solving A,B, and C with the HYPRE Euclid algorithm ILU(1),
> and D is solved with the direct solver MUMPS.
> While these were very useful to get the code working, I am now trying to
> get better parallel scaling/efficiencies and performance. HYPRE euclid does
> not seem to scale super well beyond like 60 procs, and MUMPS has very large
> memory requirements.
> Does anyone have suggestions on more scalable ILU algorithms for A,B, and
> C, or any other good alternatives?

Are these advectively dominated?

> From what I have read, multigrid methods are probably the best alternative
> for D, but I have very little experience with these and they seem to
> require a lot of parameters. Does anyone have pointers on a good setup for
> a multigrid preconditioner?

This is the easy one. If you are using DMDA, just turn on -pc_type mg and
give a number of levels and it should be fine. If not, then use GAMG and it
should be fine, You could also use Hypre Boomeramg for this since it is
optimized for the 2D Laplacian.



> Thank you and have a good day,
> -Alfredo
> --
> Alfredo Duarte
> Graduate Research Assistant
> The University of Texas at Austin

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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