Fast iterative solution of large sparse linear systems on geographically separated clusters

Abstract

Parallel asynchronous iterative algorithms exhibit features that are extremely well-suited for Grid computing, such as lack of synchronization points. Unfortunately, they also suffer from slow convergence rates. In this paper we propose using asynchronous methods as a coarse-grained preconditioner in a flexible iterative method, where the preconditioner is allowed to change in each iteration step. A full implementation of the algorithm is presented using Grid middleware that allows for both synchronous and asynchronous communication. Advantages and disadvantages of the approach are discussed. Numerical experiments on heterogeneous computing hardware demonstrate the effectiveness of the proposed algorithm on Grid computers, with application to large 2D and 3D bubbly flow problems.