Numerical conformal mappings from multiply connected regions onto slit domains using the charge simulation method

Xin Zhao; Yibin Lu

doi:10.1117/12.3000065

23 August 2023 Numerical conformal mappings from multiply connected regions onto slit domains using the charge simulation method

Xin Zhao, Yibin Lu

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Proceedings Volume 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023); 127841V (2023) https://doi.org/10.1117/12.3000065
Event: 2023 2nd International Conference on Applied Statistics, Computational Mathematics and Software Engineering (ASCMSE 2023), 2023, Kaifeng, China

Abstract

This paper proposes a numerical approach based on the charge simulation method for calculating conformal mappings from the bounded multiply connected regions onto linear slit domain and spiral slit domain. Firstly, conformal mapping formulas are defined by the normalizing conditions, and the undetermined harmonic functions in the approximate functions are represented using the first-order linear combination of complex logarithmic functions. Secondly, according to the boundary conditions, we establish the constraint equations about the charges in the charge simulation method. Finally, the charges are obtained by solving the constraint equations, which further construct a high-precision conformal mapping. Numerical examples show the effectiveness of our algorithm.

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Xin Zhao and Yibin Lu "Numerical conformal mappings from multiply connected regions onto slit domains using the charge simulation method", Proc. SPIE 12784, Second International Conference on Applied Statistics, Computational Mathematics, and Software Engineering (ASCMSE 2023), 127841V (23 August 2023); https://doi.org/10.1117/12.3000065

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