The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains

Harri Hakula; Tri Quach; Antti Rasila

doi:10.1137/17M1124164

The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains

Harri Hakula^*, Tri Quach, Antti Rasila

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Guangdong Technion - Israel Institute of Technology

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Abstract

The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key challenge addressed here is the construction of the conjugate domain and the associated conjugate problem. All variants of the method preserve the so-called reciprocal relation of the moduli. An implementation of the algorithm is given along with several examples and illustrations.

Original language	English
Pages (from-to)	A1753-A1776
Number of pages	24
Journal	SIAM Journal on Scientific Computing
Volume	41
Issue number	3
DOIs	https://doi.org/10.1137/17M1124164
Publication status	Published - 2019
MoE publication type	A1 Journal article-refereed

Keywords

numerical conformal mappings
conformal modulus
multiply connected domains
canonical domains
COMPUTATION
MODULI

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abstract = "The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key challenge addressed here is the construction of the conjugate domain and the associated conjugate problem. All variants of the method preserve the so-called reciprocal relation of the moduli. An implementation of the algorithm is given along with several examples and illustrations.",

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AU - Hakula, Harri

AU - Quach, Tri

AU - Rasila, Antti

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AB - The conjugate function method is an algorithm for numerical computation of conformal mappings for simply and doubly connected domains. In this paper the conjugate function method is generalized for multiply connected domains. The key challenge addressed here is the construction of the conjugate domain and the associated conjugate problem. All variants of the method preserve the so-called reciprocal relation of the moduli. An implementation of the algorithm is given along with several examples and illustrations.

KW - numerical conformal mappings

KW - conformal modulus

KW - multiply connected domains

KW - canonical domains

KW - COMPUTATION

KW - MODULI

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DO - 10.1137/17M1124164

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JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

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The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains

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