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An efficient \(\mathcal {O}(N)\) algorithm for computing \(\mathcal {O}(N^2)\) acoustic wave interactions in large \(N\)-obstacle three dimensional configurations

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Abstract

We develop and implement a fast and memory efficient scheme for simulating the wave interactions between large numbers of particles. This is crucial for iteratively computing a time harmonic acoustic field exterior to a configuration of the particles. The main focus of this article is on efficient computation of the wave interactions between the particles in any iterative multiple scattering approach. We develop our algorithm in four stages and demonstrate the efficiency of our interaction evaluation algorithm at each stage for configurations with several thousand convex and non-convex particles. Using this efficient approach, we simulate the full large particle wave propagation models using a flexible GMRES based inner–outer preconditioned multiple scattering iterative technique on a single compute node.

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Acknowledgments

The research of the first author was supported, in part, by Grant DMS-1216889 from the National Science Foundation. Support of the Colorado Golden Energy Computing Organization (GECO) is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80401, USA

    M. Ganesh

  2. Department of Mathematics, Macquarie University, Sydney, NSW, 2109, Australia

    S. C. Hawkins

Authors
  1. M. Ganesh
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  2. S. C. Hawkins
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Correspondence to M. Ganesh.

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Communicated by Ralf Hiptmair.

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Ganesh, M., Hawkins, S.C. An efficient \(\mathcal {O}(N)\) algorithm for computing \(\mathcal {O}(N^2)\) acoustic wave interactions in large \(N\)-obstacle three dimensional configurations. Bit Numer Math 55, 117–139 (2015). https://doi.org/10.1007/s10543-014-0491-3

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  • DOI: https://doi.org/10.1007/s10543-014-0491-3

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