Solution Procedures for Interface Problems in Acoustics and Electromagnetics
The main aim of this paper is to derive solution procedures for 2 and 3-dimensional interface problems governing the scattering of sound by a homogeneous medium and the scattering of time harmonic electromagnetic fields in air by metallic obstacles. Two i
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THEORETICAL ACOUSTICS AND NUMERICAL TECHNIQUES
EDITED BY
P. FILIPPI LABORATOIRE DE MECANIQUE ET D'ACOUSTIQUE MARSEILLE
SPRINGER-VERLAG WIEN GMBH
This work is suhject to copyright. AII rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, hroadcasting, reproduction hy photocopying machine or similar means, and storage in data hanks. © 1983 hy Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1983
ISBN 978-3-211-81786-5 DOI 10.1007/978-3-7091-4340-7
ISBN 978-3-7091-4340-7 (eBook)
CONTENTS
Page Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Integral Equations in Acoustics by P.J.T. Filippi . . . . . . . .
III
1
Finite Element Techniques for Acoustics by M. Petyt . . . . . . . . . . . . . . .
51
Wave Propagation above Layered Media by D. Habault . . . . . . . . . . . . . .
105
Boundary Element Methods and their Asymptotic Convergence by W.L. Wendland . . . . . . . . . . . . . . . . . . . . . . . .
135
Boundary Value Problems Analysis and Pseudo-Differential Operators in Acoustics by M. Durand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Parametrices, Singularities, and High Frequency Asymptotics in the Theory of Sound Waves by H.D. Alber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Solution Procedures for Interface Problems in Acoustics and Electromagnetics by E. Stephan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
PREFACE Though Acoustics is a part of continuous media mechanics, the mathematical methods recently developed in solid mechGnics are almost · never used by acousticians. This is, of course, due to a lack of scientific effort on noise and sound mathematical problems. But the main reason is that the difficulties encountered with the wave equation are strongly different from those which appear in solid mechanics. And the very convenient mathematical tools have been developed during the past fifteen years only. 1/ ACOUSTICS AND CLASSICAL MATHEMATICS Let, first, have a brief survey of the mathematical problems appearing in Acoustics. The time-dependant governing equation is of hyerbolice type (a much less simple case than the parabolic type ), and unbounded domains must be considered as soon as environmental acoustics or under-water propagation are concerned. Because of the difficulty to solve the wave equation, and because lots of noise and sound sources are periodic (or can be considered as periodic ), the Helmholtz equation is more frequently used. If the propagation domain is bounded, resonnances appear. If the propagation domain is unbounded, the total energy involved is unbounded, too. For these reasons, the use of the classical variational techniques is much less easy than for the heat equation, static solid mechanics, or incompressible fluid dynamics. Another difficulty is that as soon as energy is lost within the boundarie
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