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Numerical Conformal Mapping of Doubly Connected Regions Onto a Disc with a Circular Slit

Ali H.M. Murid, and Hu, Laey Nee, and Mohd. Nor Mohamad, (2008) Numerical Conformal Mapping of Doubly Connected Regions Onto a Disc with a Circular Slit. Journal of Quality Measurement and Analysis (JQMA), 4 (2). pp. 29-38. ISSN 1823-5670

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Official URL: http://pkukmweb.ukm.my/~ppsmfst/jqma/

Affiliations

Universiti Teknologi Malaysia. Faculty of Science. Dept. of Mathematics
Universiti Teknologi Malaysia. Faculty of Science. Dept. of Mathematics
Universiti Teknologi Malaysia. Faculty of Science. Dept. of Mathematics

Abstract

Abstract: An integral equation method based on the Neumann kernel for conformal mapping f(z) of doubly connected regions onto a unit disc with a circular slit of radius u < 1 is presented. The theoretical development is based on the boundary integral equation for conformal mapping of doubly connected region in an earlier work of the authors. In this paper, a related system of integral equations is constructed that is satisfied by f'(z) and u. For numerical experiment, the integral equation is discretized which leads to a system of nonlinear equations. The system obtained is solved simultaneously using Gauss-Newton method. Numerical implementation on a circular annulus is also presented. (Please refer to the pdf file for the maths functions)

Abstrak: Satu kaedah persamaan kamiran berdasarkan inti Neumann untuk pemetaan konformal f(z) bagi rantau berkait ganda dua ke seluruh unit cakera dengan belahan membulat berjejari u < 1 dipersembahkan. Pembangunan teori adalah berdasarkan persamaan kamiran sempadan bagi pemetaan konformal rantau berkait ganda dua dalam penyelidik pengarang sebelum ini. Dalam kertas kerja ini, suatu perhubungan sistem persamaan kamiran telah dibina yang memenuhi f'(z) dan u. Untuk kajian berangka, persamaan kamiran berkenaan telah didiskretkan menghasilkan sistem persamaan tak linear. Sistem yang diperoleh diselesaikan secara serentak dengan menggunakan kaedah Gauss-Newton. Pelaksanaan berangka terhadap anulus juga dipersembahkan. (Sila rujuk fail pdf untuk fungsi matematik.

Item Type:Journal
Keywords:Conformal mapping, Integral equation, Doubly connected region, Neumann kernel, Gauss-Newton method; Pemetaan konformal, Persamaan kamiran, Rantau berkait ganda dua, Inti Neumann, Kaedah Gauss-Newton
Subjects:Q Science, Computer Science
ID Code:9684

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