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


\({{\mathcal H}^2}\) -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.


Speedup Factor Cluster Tree Processing Node Root Cluster Communication Step 
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Open Access

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© The Author(s) 2008

Authors and Affiliations

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

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