Show simple item record

dc.contributor.authorBadreddine, Mohamed
dc.contributor.authorDeLillo, Thomas K.
dc.contributor.authorSahraei, Saman
dc.identifier.citationMohamed 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) : 55-82en_US
dc.descriptionClick on the URI link to access the article (may not be free).en_US
dc.description.abstractThis 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.en_US
dc.publisherAmerican Institute of Mathematical Sciencesen_US
dc.relation.ispartofseriesDiscrete & Continuous Dynamical Systems - B;v.24:no.1
dc.subjectNumerical conformal mappingen_US
dc.subjectMultiply connected domainsen_US
dc.subjectFornberg's methoden_US
dc.subjectGrassmann's methoden_US
dc.subjectOsculation methodsen_US
dc.subjectPotential flowen_US
dc.titleA comparison of some numerical conformal mapping methods for simply and multiply connected domainsen_US
dc.rights.holder© 2018 American Institute of Mathematical Sciencesen_US

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record