The Conjugate Function Method and Conformal Mappings in Multiply Connected Domains

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, along with several examples and illustrations are given.

Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals

“…See also [5,22,44]. Note that, if the Dirichlet-Neumann problem can be solved, then the conformal mapping can be recovered with the conjugate function method studied in [17]. We give here new numerical methods for this same case and present our results in the form of numerical tables, graphics, and analysis of algorithm performance.…”