, Volume 11, Issue 4-6, pp 237-249,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 28 Mar 2008

Distributed \({{\mathcal H}^2}\) -matrices for non-local operators

Abstract

\({{\mathcal H}^2}\) -matrices can be used to approximate dense n × n matrices resulting from the discretization of certain non-local operators (e.g., Fredholm-type integral operators) in \({{\mathcal O}(n k)}\) units of storage, where k is a parameter controlling the accuracy of the approximation. Since typically kn holds, this representation is much more efficient than the conventional representation by a two-dimensional array. For very large problem dimensions, the amount of available storage becomes a limiting factor for practical algorithms. A popular way to provide sufficiently large amounts of storage at relatively low cost is to use a cluster of inexpensive computers that are connected by a network. This paper presents a method for managing an \({{\mathcal H}^2}\) -matrix on a distributed-memory cluster that can be proven to be of almost optimal parallel efficiency.

Communicated by S. Sauter.
Dedicated to Wolfgang Hackbusch on the occasion of his 60th birthday.