Electrostatic imaging via conformal mapping

Ibrahim Akduman*, Rainer Kress

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

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. 48 703-18). We establish a convergence result for the iteration procedure and through numerical examples we illustrate the feasibility of the method.

Original languageEnglish
Pages (from-to)1659-1672
Number of pages14
JournalInverse Problems
Volume18
Issue number6
DOIs
Publication statusPublished - Dec 2002

Fingerprint

Dive into the research topics of 'Electrostatic imaging via conformal mapping'. Together they form a unique fingerprint.

Cite this