A Bidirectional Method for Numerical Conformal Mapping Based on the Charge Simulation Method

概要

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Numerical conformal mapping has been an attractive subject in numerical analysis for several decades, and is now at an exciting stage of development. Current methods fall into two groups: one for mapping a given problem domain onto a standard region, such as the unit disk, and the other for mapping in the reverse direction. No method seems to be feasible in both directions. This paper describes a bidirectional method of numerical conformal mapping between a given Jordan domain and the unit disk. The basic idea is to use the charge simulation method for solving the Dirichlet problem of Laplace's equation in order to reconstruct an approximate inverse mapping function, with the boundary correspondence established in advance. In contrast to many other methods, it does not require any nonlinear iteration procedure. It also has the following attractive features: simplicity of mathematical formulation and programming, high efficiency of computation, high accuracy of conputational results, and ease of error estimation. These are demonstrated by numerical examples for some typical problem domains.
一般社団法人情報処理学会の論文
1992-03-15