Resolution of large symmetric eigenproblems on a world-wide grid

Abstract

We propose a parallel and distributed application for the resolution of the large real symmetric eigenproblem on world-wide heterogeneous grids. It is based on the explicit restarted Lanczos algorithm which is a Krylov subspace method. We take into account the specificities of computational resources and deal with communication constraints over the internet. We propose techniques such as out-of-core and data persistence. We also show that a restarted algorithm and the combination of several paradigms of parallelism are relevant in this context. The results of the experiments stress the impact of the main numerical parameters of the Lanczos method. We also compare many platform configurations built on the top of two complementary experimental environments. We first use a realistic world-wide grid harnessing two geographical sites, in France and in Japan, interconnected by the internet. Then, we use the French national testbed Grid5000. We conclude on the scalability of our application and we forecast the next bounding factor of the implementation. It can be solved by means of a dedicated data management layer such as Omni Storage.