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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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Scattering by a Bounded Inhomogeneity

Scattering by a Bounded Inhomogeneity

Chapter:
(p.280) 11 Scattering by a Bounded Inhomogeneity
Source:
Finite Element Methods for Maxwell's Equations
Author(s):

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0011

This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the previous chapter is extended by considering the effect of discretizing the Calderon map. A Lagrange multiplier on the artificial boundary is used to couple the field exterior to the artificial sphere to the finite element method inside the sphere. This allows a decoupling of the exterior and interior problems. The discrete problem is shown to be well posed, and the convergence of the resulting finite element and Lagrange multiplier method is verified using the collective compactness approach first used in Chapter 7.

Keywords:   penetrable scatterer, Calderon map, Lagrange multiplier, error estimate

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