[petsc-users] Slow convergence while parallel computations.

[Lawrence Mitchell]

> On 1 Sep 2021, at 09:42, Наздрачёв Виктор <numbersixvs at gmail.com> wrote:
> 
> I have a 3D elasticity problem with heterogeneous properties.

What does your coefficient variation look like? How large is the contrast?

> There is unstructured grid with aspect ratio varied from 4 to 25. Zero Dirichlet BCs  are imposed on bottom face of mesh. Also, Neumann (traction) BCs are imposed on side faces. Gravity load is also accounted for. The grid I use consists of 500k cells (which is approximately 1.6M of DOFs).
> 
> The best performance and memory usage for single MPI process was obtained with HPDDM(BFBCG) solver and bjacobian + ICC (1) in subdomains as preconditioner, it took 1 m 45 s and RAM 5.0 GB. Parallel computation with 4 MPI processes took 2 m 46 s when using 5.6 GB of RAM. This because of number of iterations required to achieve the same tolerance is significantly increased.

How many iterations do you have in serial (and then in parallel)?

> I`ve also tried PCGAMG (agg) preconditioner with ICС (1) sub-precondtioner. For single MPI process, the calculation took 10 min and 3.4 GB of RAM. To improve the convergence rate, the nullspace was attached using MatNullSpaceCreateRigidBody and MatSetNearNullSpace subroutines.  This has reduced calculation time to 3 m 58 s when using 4.3 GB of RAM. Also, there is peak memory usage with 14.1 GB, which appears just before the start of the iterations. Parallel computation with 4 MPI processes took 2 m 53 s when using 8.4 GB of RAM. In that case the peak memory usage is about 22 GB.

Does the number of iterates increase in parallel? Again, how many iterations do you have?

> Are there ways to avoid decreasing of the convergence rate for bjacobi precondtioner in parallel mode? Does it make sense to use hierarchical or nested krylov methods with a local gmres solver (sub_pc_type gmres) and some sub-precondtioner (for example, sub_pc_type bjacobi)?

bjacobi is only a one-level method, so you would not expect process-independent convergence rate for this kind of problem. If the coefficient variation is not too extreme, then I would expect GAMG (or some other smoothed aggregation package, perhaps -pc_type ml (you need --download-ml)) would work well with some tuning.

If you have extremely high contrast coefficients you might need something with stronger coarse grids. If you can assemble so-called Neumann matrices (https://petsc.org/release/docs/manualpages/Mat/MATIS.html#MATIS) then you could try the geneo scheme offered by PCHPDDM.

> Is this peak memory usage expected for gamg preconditioner? is there any way to reduce it?

I think that peak memory usage comes from building the coarse grids. Can you run with `-info` and grep for GAMG, this will provide some output that more expert GAMG users can interpret.

Lawrence