Schwarz-Christoffel Mapping

Tobin A. Driscoll, Lloyd N. Trefethen

132 pages, parution le 07/06/2002

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Résumé

This book provides a comprehensive look at the Schwarz-Christoffel transformation, including its history and foundations, practical computation, common and less common variations, and many applications in fields such as electromagnetism, fluid flow, design and inverse problems, and the solution of linear systems of equations. It is an accessible resource for engineers, scientists, and applied mathematicians who seek more experience with theoretical or computational conformal mapping techniques. The most important theoretical results are stated and proved, but the emphasis throughout remains on concrete understanding and implementation, as evidenced by the 76 figures based on quantitatively correct illustrative examples. There are over 150 classical and modern reference works cited for readers needing more details. There is also a brief appendix illustrating the use of the Schwarz-Christoffel Toolbox for MATLAB, the state-of-the-art package for computation of these maps.

Contents

Introduction
The Schwarz-Christoffel idea
History

Essentials of Schwarz-Christoffel mapping
Polygons
The Schwarz-Christoffel formula
Polygons with one or two vertices
Triangles
Rectangles and elliptic functions
Crowding

Numerical methods
Side-length parameter problem
Quadrature
Inverting the map
Cross-ratio parameter problem
Mapping using cross-ratios
Software

Variations
Mapping from the disk
Mapping from a strip
Mapping from a rectangle
Exterior maps
Periodic regions and fractals
Reflections and other transformations
Riemann surfaces
Gearlike regions
Doubly connected regions
Circular-arc polygons
Curved boundaries

Applications
Why use Schwarz-Christoffel maps?
Piecewise-constant boundary conditions
Alternating Dirichlet and Neumann conditions
Oblique derivative boundary conditions
Generalized parameter problems
Free-streamline flows
Mesh generation
Polynomial approximation and matrix iterations
Symmetric multiply connected domains

L'auteur - Lloyd N. Trefethen

Lloyd N. Trefethen is Professor of Numerical Analysis and Head of the Numerical Analysis Group at the University of Oxford.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Tobin A. Driscoll, Lloyd N. Trefethen
Parution	07/06/2002
Nb. de pages	132
Format	15,5 x 23,5
Couverture	Relié
Poids	365g
Intérieur	Noir et Blanc
EAN13	9780521807265
ISBN13	978-0-521-80726-5