An interative method for conformal mappings of multiply-connected domains

Green's Functions for Multiply Connected Domains via Conformal Mapping

A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the part of the upper half-plane exterior to the problem domain onto a semi-infinite strip whose end contains K −...

QCMC: Quasi-conformal Parameterizations for Multiply-connected domains

This paper presents a method to compute the quasi-conformal parameterization (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain S onto a punctured disk DS associated with a given Beltrami differential. The Beltrami differential, which measures the conformality distortion, is a complexvalued function μ : S → C with supremum ...

A General Theorem on Conformal Mapping of Multiply Connected Domains.

A Fornberg-like Method for the Numerical Conformal Mapping of Bounded Multiply Connected Domains

A new Fornberg-like method is presented for computing conformal maps from the interior of the unit disk with m−1 circular holes to the interior of a smooth closed curve with m−1 holes bounded by smooth curves. The method is a Newton-like method for computing the boundary correspondences and the conformal moduli (centers and radii of the circles). The inner linear systems are derived from condit...

Schwarz-christoffel Mapping of Multiply Connected Domains

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m ≥ 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded, disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f...