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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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Mathematical Models of Electromagnetism

Mathematical Models of Electromagnetism

(p.1) 1 Mathematical Models of Electromagnetism
Finite Element Methods for Maxwell's Equations

Peter Monk

Oxford University Press

This chapter presents a summary of Maxwell’s equations. The time-harmonic Maxwell equations considered throughout this book are derived from the time domain system, and several linear constitutive relations are discussed. Interface conditions between materials of different electromagnetic properties and boundary conditions are described together with radiation conditions appropriate for scattering problems. Boundary value problems for a cavity with mixed impedance and perfectly conducting boundary data, and a cavity resonator are presented. Two scattering problems are defined. In particular, scattering from a bounded object using the Silver-Muller radiation condition and scattering from an object ‘buried’ in a two layer background medium using an integral radiation condition are discussed.

Keywords:   time-harmonic, cavity, scattering, radiation condition, boundary value problem

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