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 k ≪ n 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.
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Communicated by S. Sauter.
Dedicated to Wolfgang Hackbusch on the occasion of his 60th birthday.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Börm, S., Bendoraityte, J. Distributed \({{\mathcal H}^2}\) -matrices for non-local operators. Comput. Visual Sci. 11, 237–249 (2008). https://doi.org/10.1007/s00791-008-0095-z
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DOI: https://doi.org/10.1007/s00791-008-0095-z