Parallel Scientific Computing on Loosely Coupled Networks of Computers

Abstract

Efficiently solving large sparse linear systems on loosely coupled networks of computers is a rich and vibrant field of research. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. Designing efficient numerical algorithms for said systems is a complex process that brings together many different scientific disciplines. This book chapter is divided into two distinct parts. The purpose of the first half (Sect. 2–4) is to give a bird’s view of the issues pertaining to designing efficient numerical algorithms for Grid computing. It kicks off by clearly stating the problemand exposing the various bottlenecks, subsequently followed by the presentation of potential solutions. Thus, the stage is set and Sect. 3 proceeds by detailing classical iterative solution methods, along with the concept of asynchronism, which is a highly favorable quality in the context of Grid computing. The first half is wrapped up by explaining how asynchronism can be introduced into faster but more complicated subspace methods. The general idea is that by using an asynchronous method as a preconditioner, the best of both worlds can be combined. The advantages and disadvantages of this approach are discussed in minute detail. The second half (Sect. 5) contains discussions on the various intricacies related to implementing the proposed algorithm on Grid computers. Section 6 gives some concluding remarks along with suggestions for further reading.