A parallel implementation of the Glowinski-Pironneau algorithm for the modified Stokes problem.

摘要

In this dissertation we consider a parallel implementation of the Glowinski-Pironneau algorithm for the modified Stokes problem. In particular, we motivate this effort by demonstrating the occurrence of the modified Stokes problem in the time dependent viscoelastic Oldroyd flow setting using Saramito's splitting. We then present an analysis of the Glowinski-Pironneau pressure decomposition for the modified Stokes problem—including numerical error estimates. Next we discuss our parallel finite element method implementation of the pressure decomposition approach. Finally, we present numerical results including errors and performance measures. These measures are also compared with results for a coupled velocity-pressure modified Stokes solver using a publicly available parallel solver.