Fast algorithms and their applications to numerical quasiconformal mappings of doubly connected domains onto annuli /
A numerical method for quasiconformal mapping of doubly
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736824571&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | A numerical method for quasiconformal mapping of doubly connected domains onto annuli is presented. The annulus itself is not known a priori and is determined as part of the solution procedure. The numerical method requires solving a sequence of inhomogeneous Beltrami equations, each within a different annulus, in an iterative mode. The annulus within which the equation is being solved is also updated during the iterations using an updating procedure based on the bisection method. This quasiconformal mapping method is based on Daripa's method of quasiconformal mapping of simply connected domains onto unit disks. The performance of the quasiconformal mapping algorithm has been demonstrated on several doubly connected domains with two different complex dilations. The solution of the Beltrami equation in an annulus requires evaluating two singular integral operators. Fast algorithms for their accurate evaluation are presented. These are based on extension of a fast algorithm of Daripa. These algorithms are based on some recursive relations in Fourier space and the FFT (fast Fourier transform), and have theoretical computational complexity of order log N per point. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | xi, 119 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 110-112. |