[petsc-users] Failure of MUMPS

[Jed Brown]

Dave May <dave.mayhem23 at gmail.com> writes:

> * Rudi, Johann, Georg Stadler, and Omar Ghattas. "Weighted BFBT
> Preconditioner for Stokes Flow Problems with Highly Heterogeneous
> Viscosity." SIAM Journal on Scientific Computing 39.5 (2017): S272-S297.

Somehow the SIAM version of the abstract says this is Q_k \times
Q_{k-1}^{disc} (an unstable element) despite both arXiv versions saying
Q_k \times P_{k-1}^{disc} (the stable element that they actually use).

  https://epubs.siam.org/doi/pdf/10.1137/16M108450X

This weighting scheme (using a lumped velocity mass matrix scaled by
viscosity) would be good work to add to PCLSC.

> Note that in the Rudi et al papers, due the highly variable nature of the
> viscosity, the authors advocate using a more complex definition of the
> preconditioner for the Schur complement. Whether you need to use their
> approach is dependent on the nature of the problem you are solving.