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

Mathematics with Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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
Journal	SIAM Journal on Scientific Computing
Volume	41
Issue number	3
DOIs	https://doi.org/10.1137/17M1124164
State	Published - 2019

Keywords

Canonical domains
Conformal modulus
Multiply connected domains
Numerical conformal mappings

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10.1137/17M1124164

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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.",

keywords = "Canonical domains, Conformal modulus, Multiply connected domains, Numerical conformal mappings",

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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 - Canonical domains

KW - Conformal modulus

KW - Multiply connected domains

KW - Numerical conformal mappings

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The conjugate function method and conformal mappings in multiply connected domains

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Keywords

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