Ibrahim Akduman and Rainer Kress 2002 Inverse Problems 18 1659 doi:10.1088/0266-5611/18/6/315
Ibrahim Akduman1 and Rainer Kress2
Show affiliationsWe 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.
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
35F30 Boundary value problems for nonlinear first-order PDE
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
Issue 6 (December 2002)
Received 17 May 2002, in final form 3 October 2002
Published 1 November 2002
Ibrahim Akduman and Rainer Kress 2002 Inverse Problems 18 1659
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