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Finite Element Methods for Maxwell's Equations$
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Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

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Classical Scattering Theory

Classical Scattering Theory

Chapter:
(p.225) 9 Classical Scattering Theory
Source:
Finite Element Methods for Maxwell's Equations
Author(s):

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0009

This chapter presents basic tools for studying the scattering problem. The Stratton-Chu integral representation of the electromagnetic field is derived as well as the far field pattern of the scattered wave. Using vector wave functions related to spherical Bessel functions, scattering by a perfectly conducting sphere is analysed, and Rellich’s lemma is proven. The mapping properties of the exterior Calderon operator that maps the surface electric current to the surface magnetic current are also derived, leading to the Mie solution of the scattering problem. This solution is useful as an exact solution for testing scattering codes.

Keywords:   Stratton-Chu formula, integral representation, far field pattern, vector wave function, scattering by a sphere, spherical Bessel functions, Rellich’s lemma

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