Electrostatic imaging via conformal mapping

Authors: Akduman I.¹; Kress R.²

Source: Inverse Problems, Volume 18, Number 6, 2002 , pp. 1659-1672(14)

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Abstract:

We present the solution of an inverse boundary value problem for harmonic functions arising in electrostatic imaging through conformal mapping techniques. The numerical method consists of two parts. In a first step, by successive approximations a nonlinear equation is solved to determine the boundary values of a holomorphic function on the outer boundary circle of an annulus. Then in a second step an ill-posed Cauchy problem is solved to determine the holomorphic function in the annulus. The method extends and modifies an earlier analysis of Idemen and Akduman (Idemen M and Akduman I 1988 SIAM J. Appl. Math.48703-18). We establish a convergence result for the iteration procedure and through numerical examples we illustrate the feasibility of the method.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Istanbul Technical University, Electrical and Electronics Engineering Faculty, Maslak 80626, Istanbul, Turkey 2: Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, Germany

Publication date: 2002-01-01