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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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The Scattering Problem Using Calderon Maps

The Scattering Problem Using Calderon Maps

Chapter:
(p.261) 10 The Scattering Problem Using Calderon Maps
Source:
Finite Element Methods for Maxwell's Equations
Author(s):

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0010

This chapter presents a finite element method for scattering by a bounded scatterer in an infinite homogeneous background. The first task is to reduce the problem to a bounded domain, and in this algorithm, an artificial sphere surrounds the scatterer. Outside the scatterer and within the sphere, the edge finite element introduced in Chapter 7 is used to discretize the field. The field outside the sphere is taken into account using the Calderon map derived in the previous chapter. This variational formulation is shown to have a unique solution that agrees with the solution of the scattering problem. A third method of analysis (compared to the two in Chapter 7) is used to prove convergence via the Babuska-Brezzi theory outlined in Chapter 2.

Keywords:   bounded obstacle, Calderon map, error estimate

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