The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains

Harri Hakula*, Tri Quach, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 languageEnglish
Pages (from-to)A1753-A1776
Number of pages24
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed


  • numerical conformal mappings
  • conformal modulus
  • multiply connected domains
  • canonical domains

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