دانلود کتاب 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 ontoannuli is presented. The annulus itself is not known a priori and is determined aspart of the solution procedure. The numerical method requires solving a sequenceof inhomogeneous Beltrami equations, each within a different annulus, in an iterativemode. The annulus within which the equation is being solved is also updatedduring the iterations using an updating procedure based on the bisection method.This quasiconformal mapping method is based on Daripa's method of quasiconformalmapping of simply connected domains onto unit disks. The performance ofthe quasiconformal mapping algorithm has been demonstrated on several doublyconnected domains with two different complex dilations.The solution of the Beltrami equation in an annulus requires evaluating twosingular integral operators. Fast algorithms for their accurate evaluation are presented.These are based on extension of a fast algorithm of Daripa. These algorithmsare based on some recursive relations in Fourier space and the FFT (fastFourier transform), and have theoretical computational complexity of order log Nper point.