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.
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机译：我们提出了通过保形映射技术在静电成像中产生的谐波函数的逆边界值问题的解决方案。数值方法包括两部分。第一步，通过逐次逼近，求解一个非线性方程，以确定圆环外边界圆上全纯函数的边界值。然后，在第二步中，解决不适定的柯西问题，以确定环中的全纯函数。该方法扩展并修改了对Idemen和Akduman的早期分析（Idemen M和Akduman I 1988 SIAM J. Appl。Math。48 703-18）。我们为迭代过程建立了收敛结果，并通过数值例子说明了该方法的可行性。
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