Conjugate Function Method and Conformal Mappings in Multiply Connected Domains
It extends a known numerical method to a broader class of domains, offering a new tool for computational conformal mapping in complex analysis.
The paper generalizes the conjugate function method for numerical conformal mapping to multiply connected domains, preserving the reciprocal relation of moduli, and provides an implementation with examples.
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, along with several examples and illustrations are given.