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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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Inverse Problems

Inverse Problems

Chapter:
(p.394) 14 Inverse Problems
Source:
Finite Element Methods for Maxwell's Equations
Author(s):

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0014

This final chapter introduces an inverse electromagnetic reconstruction problem of finding the shape of a scatterer from far field data. It focuses on the Linear Sampling Method that reduces the problem to the solution of many linear integral equations. Using techniques from earlier in the book as well as reciprocity of the solution, the uniqueness of the solution of the inverse problem is proved. The inverse problem is shown to be ill-posed, but a partial mathematical justification of the inversion scheme is shown. Details of the Morozov discrepancy principle and Tikhonov regularization scheme used to approximate the integral equations are given, and numerical results are provided to illustrate the scheme.

Keywords:   inverse scattering, shape reconstruction, reciprocity, uniqueness, regularization

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