# [petsc-users] Overcoming slow convergence with GMRES+Hypre BoomerAMG

Thu Mar 2 02:57:37 CST 2023

```Can you give us a bit more detail on your equations?

* You are going to want to use FieldSplit.

* AMG usually takes some effort to get working well. You want to start
simple, even just a Lapacian or two decoupled Laplacians in your code to
get the expected MG performance. Then add realistic geometry, then more
tems, etc., and ramp up to what you want to do and we can help you address
problems that arise at each step. Verify the results at each step.

Mark

On Thu, Mar 2, 2023 at 5:51 AM Christopher, Joshua via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Hello,
>
> I am trying to solve the leaky-dielectric model equations with PETSc using
> a second-order discretization scheme (with limiting to first order as
> needed) using the finite volume method. The leaky dielectric model is a
> coupled system of two equations, consisting of a Poisson equation and a
> convection-diffusion equation.  I have tested on small problems with simple
> geometry (~1000 DoFs) using:
>
> -ksp_type gmres
> -pc_type hypre
> -pc_hypre_type boomeramg
>
> and I get RTOL convergence to 1.e-5 in about 4 iterations. I tested this
> in parallel with 2 cores, but also previously was able to use successfully
> use a direct solver in serial to solve this problem. When I scale up to my
> production problem, I get significantly worse convergence. My production
> problem has ~3 million DoFs, more complex geometry, and is solved on ~100
> cores across two nodes. The boundary conditions change a little because of
> the geometry, but are of the same classifications (e.g. only Dirichlet and
> Neumann). On the production case, I am needing 600-4000 iterations to
> converge. I've attached the output from the first solve that took 658
> iterations to converge, using the following output options:
>
> -ksp_view_pre
> -ksp_view
> -ksp_converged_reason
> -ksp_monitor_true_residual
> -ksp_test_null_space
>
> My matrix is non-symmetric, the condition number can be around 10e6, and
> the eigenvalues reported by PETSc have been real and positive (using
> -ksp_view_eigenvalues).
>
> I have tried using other preconditions (superlu, mumps, gamg, mg) but
> hypre+boomeramg has performed the best so far. The literature seems to
> indicate that AMG is the best approach for solving these equations in a
> coupled fashion.
>
> Do you have any advice on speeding up the convergence of this system?
>
> Thank you,
> Joshua
>
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