Parameter identification for Maxwell's equations

Jais, Mathias 2006. Parameter identification for Maxwell's equations. PhD Thesis, Cardiff University.

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Abstract

In this work we present a variational algorithm to determine the parameters iir(x) and er(x) in the Maxwell system VxE + k xTH = 0, V x H - kerE = 0 in a body Q from boundary measurements of electromagnetic pairs (n x En dci,n x Hn dn), n= 1,2,…, where n is the outer unit normal. We show that this inverse problem can be solved by minimizing a positive functional C7(m,c) and using a conjugate gradient scheme. Apart from implementations with global boundary, we also consider the case of partial boundary, where we have only data available on a subset T C dQ. Further do we develop uniqueness results, to show that the given data (n x En dn, n x Hn dn), n = 1,2,…, is a sufficient basis to solve the inverse problem. We investigate the uniqueness properties of the inverse problem in the case of global boundary data as well as in the case of partial boundary data. To show the effectivness and the stability of our approach we present various numerical results with noisy data. Finally we outline an alternative method, where one is only interested in recovering the support of the functions fi l 1 and er 1.

Item Type:	Thesis (PhD)
Status:	Unpublished
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
ISBN:	9781303208621
Date of First Compliant Deposit:	30 March 2016
Last Modified:	12 Feb 2016 23:12
URI:	https://orca.cardiff.ac.uk/id/eprint/54581

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