NUMERICAL CONFORMAL MAPPING

Domain Decomposition And The Mapping Of Quadrilaterals

By: Nicolas Papamichael, Nikos Stylianopoulos

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Hardcover | 1 June 2010

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Hardcover
244 Pages

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22.86 x 15.24 x 1.42

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This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications.The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments.This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.

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Preface	p. vii
Standard Conformal Mappings and Software	p. 1
Introduction	p. 1
The mapping of simply-connected domains	p. 2
The mapping of doubly-connected domains	p. 9
Numerical conformal mapping	p. 13
The Bergman kernel method	p. 16
The integral equation method of Symm	p. 21
Schwarz-Christoffel mappings	p. 25
Conjugate periodic functions on an annulus	p. 31
The method of Garrick	p. 35
Numerical examples	p. 44
Conformal Modules of Quadrilaterals	p. 51
Basic definitions and properties	p. 51
Physical interpretation and applications	p. 55
Further properties	p. 61
The conventional method	p. 71
The crowding phenomenon	p. 75
Examples	p. 80
A finite-element method	p. 86
A modified Schwarz-Christoffel method	p. 88
Cross-ratios and Delaunay triangulation (CRDT)	p. 90
The method of Garrick for special quadrilaterals	p. 91
The use of Laplacian solvers	p. 100
Domain Decomposition for Special Quadrilaterals	p. 105
Introduction	p. 105
Error estimation via the theory of the Garrick method	p. 107
Error estimates for conformal modules	p. 116
Error estimates for the full conformal mapping	p. 130
Domain Decomposition for General Quadrilaterals	p. 141
Introduction	p. 141
Error estimates for conformal modules	p. 142
Curvilinear crosscuts	p. 154
The asymptotic behavior of conformal modules	p. 166
Engineering rules for conformal modules	p. 177
Error estimates for the full conformal mapping	p. 187
Bibliography	p. 211
Index	p. 227
Table of Contents provided by Ingram. All Rights Reserved.

NUMERICAL CONFORMAL MAPPING

Domain Decomposition And The Mapping Of Quadrilaterals

At a Glance

Hardcover

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