A Fornberg-like method for the numerical conformal mapping of bounded multiply connected domains
Abstract
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 conditions for analytic extension of functions
de ned on the circles to the interior domain. These systems are N-point trigonometric
discretizations of the identity plus a compact operator and are solved efficiently with the
conjugate gradient method at a cost of O(N²)per step. Two formulations of the map are
given: the rst uses a disk with circular holes, and the second uses an annulus with circular
holes. Some numerical examples are given.
Description
Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics