http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Fast algorithms and their applications to numerical quasiconformal mappings of doubly connected domains onto annuli
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
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Includes bibliographical references: pages 110-112.