  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.
