Exploiting the flexibility of IDR(s) for grid computing

Abstract

The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s) variant with an a-synchronous preconditioning iteration to further improve the performance of IDR(s) on a grid computer. A-synchronous preconditioners do not require expensive synchronisation and adapt to volatile computational resources, and are therefore well-suited for such a computational environment. However, an a-synchronous preconditioning operation is also non-constant by nature: the preconditioner changes in every iteration. The success of the combination of IDR(s) with an a-synchronous preconditioner therefore depends on the flexibility of IDR(s). We will explain why IDR(s) can be used as a flexible method, and we will successfully use the combination of IDR(s) with an a-synchronous preconditioner for solving large convection-diffusion problems. The numerical experiments are performed on the DAS-3 grid computer, which is composed of five geographically separated parallel clusters.