Parallel scientific computing on loosely coupled networks of computers

Abstract Efficiently solving large sparse linear systems on loosely coupled net-works of computers is a rich and vibrant field of research. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous al-gorithmic 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 algo-rithms for Grid computing. It kicks off by clearly stating the problem and exposing the various bottlenecks, subsequently followed by the presentation of potential so-lutions. 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 fa-vorable 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 disad