A parallel implementation of the Hermitian and skew-Hermitian splitting preconditioner for generalized saddle point problems

Abstract

We study a parallel implementation of different preconditioning techniques for the iterative solution of saddle point problems that arise in the finite element and finite difference discretization of the incompressible Navier-Stokes equations.

In this thesis we study variants of the Hermitian and skew-Hermitian splitting preconditioner. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to the finite element (Q2-P1) and MAC discretization of the Stokes and Oseen problems. We analyze the eigenvalue distribution of the preconditioned matrices. Then we assess variants of the preconditioner aimed at achieving optimal parameter of the algorithm regarding iteration number and computational times.

Numerical experiments involve many model problems in two and three dimensions. The obtained results demonstrate the robustness and the efficiency of these preconditioners. We analyze the parallel performance of all the experiments with respect to wall-clock time, and the framework demonstrates good and strong scalability results for up to 64 cores.