Jump to ContentJump to Main Navigation
Finite Element Methods for Maxwell's Equations$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 09 July 2020

Inverse Problems

Inverse Problems

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

Peter Monk

Oxford University Press

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .