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Parallel \({\mathcal {H}}\)-matrix arithmetic on distributed-memory systems

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Computing and Visualization in Science

Abstract

In the last decade, the hierarchical matrix technique was introduced to deal with dense matrices in an efficient way. It provides a data-sparse format and allows an approximate matrix algebra of nearly optimal complexity. This paper is concerned with utilizing multiple processors to gain further speedup for the \({\mathcal {H}}\)-matrix algebra, namely matrix truncation, matrix–vector multiplication, matrix–matrix multiplication, and inversion. One of the most cost-effective solution for large-scale computation is distributed computing. Distribute-memory architectures provide an inexpensive way for an organization to obtain parallel capabilities as they are increasingly popular. In this paper, we introduce a new distribution scheme for \({\mathcal {H}}\)-matrices based on the corresponding index set. Numerical experiments applied to a BEM model will complement our complexity analysis.

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Acknowledgments

The author would like to thank Dr. Ronald Kriemann for several fruitful discussions on this paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Bahonar University of Kerman, P.O.Box 76169-14111, Kerman, Iran

    Mohammad Izadi

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  1. Mohammad Izadi
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Correspondence to Mohammad Izadi.

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Communicated by: Wolfgang Hackbusch.

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Izadi, M. Parallel \({\mathcal {H}}\)-matrix arithmetic on distributed-memory systems. Comput. Visual Sci. 15, 87–97 (2012). https://doi.org/10.1007/s00791-013-0198-z

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  • DOI: https://doi.org/10.1007/s00791-013-0198-z

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