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Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics

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Topics in Computational Wave Propagation

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 31))

Abstract

We review a set of algorithms and methodologies developed recently for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, Fast Fourier Transforms and highly accurate high-frequency integrators, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers — even in cases in which the scatterers contain geometric singularities such as comers and edges. All of the solvers presented here exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. In particular, our approach to direct solution of integral equations results in algorithms that can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects — a goal, otherwise achievable today only by super-computing. The high-order high-frequency methods we present, in turn, are efficient where our direct methods become costly, thus leading to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum.

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Author information

Authors and Affiliations

  1. Applied and Computational Mathematics, Caltech, Pasadena, CA, 91125, USA

    Oscar P. Bruno

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  1. Oscar P. Bruno
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Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, Richmond Street 26, Glasgow, G1 1XH, UK

    Mark Ainsworth  & Penny Davies  & 

  2. Department of Mathematics, Heriot-Watt University, Riccarton Campus, EH14 4AS, Edinburgh, UK

    Dugald Duncan  & Bryan Rynne  & 

  3. Department of Mathematics and Computer Sciences, Colorado School of Mines, 80401-1887, Golden, USA

    Paul Martin

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Bruno, O.P. (2003). Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics. In: Ainsworth, M., Davies, P., Duncan, D., Rynne, B., Martin, P. (eds) Topics in Computational Wave Propagation. Lecture Notes in Computational Science and Engineering, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55483-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-55483-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00744-9

  • Online ISBN: 978-3-642-55483-4

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