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Computing and Visualization in Science

, Volume 11, Issue 4–6, pp 237–249 | Cite as

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

  • Steffen BörmEmail author
  • Joana Bendoraityte
Open Access
Regular article

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.

Keywords

Speedup Factor Cluster Tree Processing Node Root Cluster Communication Step 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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