Overlapping Multi-Subdomain Asynchronous Fixed Point Methods for Elliptic Boundary Value Problems

Abstract

We present and analyze asynchronous iterations for the solution of second order elliptic partial differential equations based on an overlapping domain decomposition. Asynchronous iterations constitute a general framework for fixed point methods, where the considered fixed point mapping is defined on a product space. Our general formulation includes standard relaxation algorithms such as Jacobi and Gauss-Seidel and their block versions. Indeed the block versions can be related to the additive and multiplicative Schwarz method respectively. In addition to the standard situations, asynchronous iterations can describe more involved synchronous or asynchronous parallel algorithms. For recent developments for the multi-subdomain multiplicative Schwarz (Gauss-Seidel) method we refer to [1] and [2]. For truly asynchronous methods for overlapping subdomain decompositions we refer to [7] for first partial results. One important feature of the results presented here is the use of weighted L norms, which allows us to obtain a stronger convergence property than

Cite this paper

@inproceedings{Miellou1998OverlappingMA, title={Overlapping Multi-Subdomain Asynchronous Fixed Point Methods for Elliptic Boundary Value Problems}, author={J.- C. Miellou and Martin J. Gander}, year={1998} }