A comparison of some numerical conformal mapping methods for simply and multiply connected domains

No Thumbnail Available
Authors
Badreddine, Mohamed
DeLillo, Thomas K.
Sahraei, Saman
Advisors
Issue Date
2019-01
Type
Article
Keywords
Numerical conformal mapping , Multiply connected domains , Fornberg's method , Grassmann's method , Osculation methods , Potential flow
Research Projects
Organizational Units
Journal Issue
Citation
Mohamed Badreddine, Thomas K. DeLillo, Saman Sahraei. A Comparison of some numerical conformal mapping methods for simply and multiply connected domains. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 55-82
Abstract

This paper compares some methods for computing conformal maps from simply and multiply connected domains bounded by circles to target domains bounded by smooth curves and curves with corners. We discuss the use of explicit preliminary maps, including the osculation method of Grassmann, to first conformally map the target domain to a more nearly circular domain. The Fourier series method due to Fornberg and its generalization to multiply connected domains are then applied to compute the maps to the nearly circular domains. The final map is represented as a composition of the Fourier/Laurent series with the inverted explicit preliminary maps. A method for systematically removing corners with power maps is also implemented and composed with the Fornberg maps. The use of explict maps has been suggested often in the past, but has rarely been carefully studied, especially for the multiply connected case. Using Fourier series to represent conformal maps from domains bounded by circles to more general domains has certain computational advantages, such as the use of fast methods. However, if the target domain has elongated sections or corners, the mapping problems can suffer from severe ill-conditioning or loss of accuracy. The purpose of this paper is to illustrate some of these practical possibilites and limitations.

Table of Contents
Description
Click on the URI link to access the article (may not be free).
Publisher
American Institute of Mathematical Sciences
Journal
Book Title
Series
Discrete & Continuous Dynamical Systems - B;v.24:no.1
PubMed ID
DOI
ISSN
1531-3492
EISSN