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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

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

Peter Monk

Oxford University Press

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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