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A Numerical Method for Conformal Mappings

Fornberg, Bengt (1980) A Numerical Method for Conformal Mappings. SIAM Journal on Scientific and Statistical Computing, 1 (3). pp. 386-400. ISSN 0196-5204. doi:10.1137/0901027.

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A numerical technique is presented for calculating the Taylor coefficients of the analytic function which maps the unit circle onto a region bounded by any smooth simply connected curve. The method involves a quadratically convergent outer iteration and a super-linearly convergent inner iteration. If N complex points are distributed equidistantly around the periphery of the unit circle, their images on the edge of the mapped region, together with approximations for the N/2 first Taylor coefficients, are obtained in O(Nlog N) operations. A calculation of time-dependent waves on deep water is discussed as an example of the potential applications of the method.

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Additional Information:© 1980 Society for Industrial and Applied Mathematics. Received by the editors January 24, 1980. This research was supported by Control Data Corporation and by the U.S. Department of Energy Office of Basic Energy Sciences.
Funding AgencyGrant Number
Control Data CorporationUNSPECIFIED
Department of EnergyUNSPECIFIED
Subject Keywords:conformal mapping; Fast Fourier transform; conjugate gradients; water waves
Issue or Number:3
Record Number:CaltechAUTHORS:FORsiamjssc80
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12996
Deposited On:15 Jan 2009 00:51
Last Modified:08 Nov 2021 22:34

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