[Trilinos-Users] MueLu preconditioning for mixed FEM methods

[Brian Granzow]

Hi all,

I am using Tpetra, Belos, and MueLu in a manner very similar to the example:

https://github.com/trilinos/Trilinos/blob/master/packages/muelu/example/basic/Simple.cpp

to solve a linear system that arises from a mixed
displacement-pressure mechanics formulation, where displacements are
interpolated using 2nd order Lagrange elements and pressures are
interpolated using 1st order Lagrange elements.

I am using MueLu to precondition the linear system and the
Belos::BlockGmresSolMgr to solve the linear system with GMRES
iterations.

I am using MueLu incredibly naively, in that I am not specifying any
input parameters and letting MueLu choose all default values. I am
using the method MueLu::createTpetraPreconditioner(...) to create the
MueLu preconditioner, as linked below:

https://github.com/trilinos/Trilinos/blob/master/packages/muelu/adapters/tpetra/MueLu_CreateTpetraPreconditioner.hpp#L49

My example problem has ~70,000 rows/cols. For the linear solve, Belos
converges to a tolerance of 1.0e-6 in around 420 GMRES iterations.
This behavior is about the same in serial as in parallel with 4 parts,
where in serial the problem converges in slightly fewer GMRES
iterations. Given the relatively small size of the problem, this
number of GMRES iterations seems slightly high to me.

Given this information, I have a few questions:

(1) Has anyone used MueLu to successfully precondition FEM matrices
where Taylor-Hood type elements are used and, if so, would you be
willing to share your strategy for preconditioning your linear
systems?

(2) I am not passing in the optional coordinate and null space
arguments to the method MueLu::createTpetraPreconditioner(...) method.
Would I benefit greatly from doing so?

Thank you,
Brian