NUMERICAL CONFORMAL MAPPING VIA CHEBYSHEV WEIGHTED SOLUTIONS OF SYMM INTEGRAL-EQUATION

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:46

Article

HOUGH, DM ; LEVESLEY, J ; CHANDLERWILDE, SN

关键词: NUMERICAL CONFORMAL MAPPING;    1ST-KIND INTEGRAL EQUATION;    FAST FOURIER TRANSFORM;    CHEBYSHEV POLYNOMIALS;    CORNER SINGULARITIES;   

DOI  :  10.1016/0377-0427(93)90285-J

来源: Elsevier

【 摘 要 】

A numerical method is described for the conformal mapping of simply connected domains wit piecewise analytic boundary. The method is based on the first-kind integral equation formulation of Symm (1966). On each component analytic arc of the boundary, the end point singularities of the unknown source density sigma are annihilated by introducing the classical Chebyshev weight w, so that sigma/w may be approximated by a finite Chebyshev polynomial series. The coefficients in these series are determined by collocation. The method, which provides a problem-independent treatment of end point singularities, has the advantages that all nonsingular integrals may be efficiently computed via the FFT and singular integrals are known in simple and exact form. Numerical examples illustrate the effectiveness of the method and also provide experimental confirmation of the partial error analysis of the authors (forthcoming paper).

【 授权许可】

Free