Numerical Conformal Mapping with Rational Functions

New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the Dirichlet problem is solved by the “lightning Laplace solver” wit...

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Bibliographic Details
Published in:Computational methods and function theory Vol. 20; no. 3-4; pp. 369 - 387
Main Author: Trefethen, Lloyd N.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Springer Nature B.V
Subjects:
Algorithms
Analysis
Computational Mathematics and Numerical Analysis
Conformal mapping
Dirichlet problem
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Polygons
Rational functions
Rational approximation
Conformal mapping
Lightning Laplace solver
Schwarz–Christoffel formula
30C30
41A20
AAA approximation
65E05
circular polygon
ISSN:1617-9447, 2195-3724
Online Access:Get full text
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Summary:New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the Dirichlet problem is solved by the “lightning Laplace solver” with poles exponentially clustered near each singularity. For polygons and circular polygons, further simplifications are possible.
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ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-020-00325-w