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High-Order Methods for High-Frequency Scattering Applications

Bruno, O. P. and Reitich, F. (2008) High-Order Methods for High-Frequency Scattering Applications. In: Modeling and Computations in Electromagnetics: A Volume Dedicated to Jean-Claude Nédélec. Lecture Notes in Computational Science and Engineering. No.59. Springer , Berlin, pp. 129-163. ISBN 978-3-540-73777-3.

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The problem of simulating the scattering of (acoustic, electromagnetic, elastic) waves has provided a particularly sustained, demanding and motivating challenge for the development of efficient and accurate numerical methods since the advent of computers. The classical issues present in most other applications, such as those related to the environmental and/or geometrical intricacies of the media in which quantities of interest are defined, are augmented in the context of wave propagation by the intrinsic complexities (i.e. oscillations) of the quantities themselves. Still, very efficient methodologies have been devised, particularly in the last twenty years, to simulate wave processes in rather complex settings. These techniques can be based, for instance, on finite elements (see e.g. [34, 35, 46] and the references therein), finite differences [40, 49] or boundary integral equations [4, 8, 11, 16, 25], and they can, today, effectively address these problems, with a high degree of accuracy, in domains that can span tens or perhaps even a few hundred wavelengths. The very nature of these classical approaches, however, limits their applicability at higher frequencies since the numerical resolution of field oscillations translates in a commensurately higher number of degrees of freedom and this, in turn, can easily lead to impractical computational times. In this chapter we review some recently proposed methodologies [5, 13–15, 29] that can overcome these limitations while retaining the mathematical rigor of classical numerical procedures.

Item Type:Book Section
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Bruno, O. P.0000-0001-8369-3014
Additional Information:© 2008 Springer-Verlag Berlin Heidelberg.
Subject Keywords:Circular Cylinder; Target Point; Boundary Integral Equation; Geometrical Optic; Eikonal Equation
Series Name:Lecture Notes in Computational Science and Engineering
Issue or Number:59
Record Number:CaltechAUTHORS:20181105-150853442
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90651
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 18:35
Last Modified:16 Nov 2021 03:34

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