# Bidirectional numerical conformal mapping based on the dipole simulation method

## TL;DR

This paper introduces a new bidirectional numerical conformal mapping method based on the dipole simulation approach, addressing limitations of existing techniques and providing theoretical error analysis and numerical validation.

## Contribution

It presents a novel numerical scheme for conformal mapping using the dipole simulation method, including error estimates and singular point arrangements.

## Key findings

- The proposed method effectively computes conformal mappings.
- Mathematical theorems on approximation error are established.
- Numerical results demonstrate the method's accuracy and efficiency.

## Abstract

Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for computing conformal mappings based on the method of fundamental solutions, and it has been applied to several regions with great success. However, there are some difficulties in constructing a suitable conjugate harmonic function; therefore, it is required a little of craftmanship. In this paper, we construct another numerical scheme for computing conformal mappings based on the dipole simulation method and give mathematical theorems on the approximation error and the arrangements of the singular points. Several numerical results are also presented in order to ensure the effectiveness of our proposed method.