Some Domain Decomposition and Iterative Refinement Algorithms for Elliptic Finite Element Problems

Abstract

In this contribution, we report on some results recently obtained in joint work with Maksymilian Dryja. We first study an additive variant of Schwarz' alternating algorithm and establish that a fast method of this kind can be devised which is optimal in the sense that the number of conjugate gradient iterations required, to reach a certain tolerance, is independent of the mesh size as well as the number of subregions.