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Boundary integral equations for magnetic screens in ℝ3*

Published online by Cambridge University Press:  14 November 2011

Ernst P. Stephan
Ernst P. Stephan
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.
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Synopsis

A boundary integral method is developed for the scattering of electromagnetic waves at thin obstacles. The exterior boundary value problem for the vector Helmholtz equation with given Neumann data on an open surface piece (screen S) is converted into a system of integral equations for the jumps of the tangential component of the field and its divergence across the screen. A slight modification of the Cauchy data yields a strongly elliptic system of pseudodifferential equations on S which can therefore be used for numerical computations using Galerkin's procedure. The resulting boundary integral equations are analysed using pseudodifferential operator calculus. The principal symbol concept, together with the Wiener–Hopf technique, are used to derive existence and regularity results for the solutions to the boundary integral equations. Quasi-optimal error estimates in the energy norm are given for the numerical scheme.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 102 , Issue 3-4 , 1986 , pp. 189 - 210
Copyright
Copyright © Royal Society of Edinburgh 1986

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