An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels

An integral equation method based on the Kerzman-Stein and the Neumann kernels for conformal mapping of doubly connected regions onto an annulus is presented. The theoretical development is based on the boundary integral equations for conformal mapping of doubly connected regions derived by Murid an...

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Main Author:	Mohamed, Nurul Akmal
Format:	Thesis
Language:	English
Published:	2007
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/2153/1/NurulAkmalMohamedMFS20071.pdf
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spelling	my-utm-ep.21532018-07-17T06:20:55Z An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels 2007-04 Mohamed, Nurul Akmal QA Mathematics An integral equation method based on the Kerzman-Stein and the Neumann kernels for conformal mapping of doubly connected regions onto an annulus is presented. The theoretical development is based on the boundary integral equations for conformal mapping of doubly connected regions derived by Murid and Razali (1999). However, the integral equations are not in the form of Fredholm integral equation and no numerical experiments are reported. If some information on the zero and singularity of the mapping function is known, then the integral equations can be reduced to the numerically tractable Fredholm integral equations involving the unknown inner radius. For numerical experiments, discretizing the integral equations lead to a system of non-linear equations. The system obtained is solved simultaneously using Newton’s iterative method. Further modification of the integral equations of Murid and Razali (1999) has lead to an efficient and numerically tractable integral equations which involve the unknown inner radius. These integral equations are feasible for all doubly connected regions with smooth boundaries regardless of the information on the zeroes and singularities of the mapping functions. Discretizing the integral equations lead to an over determined system of non-linear equations which is solved using an optimization technique. Numerical implementations on some test regions are also presented. 2007-04 Thesis http://eprints.utm.my/id/eprint/2153/ http://eprints.utm.my/id/eprint/2153/1/NurulAkmalMohamedMFS20071.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mohamed, Nurul Akmal An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
description	An integral equation method based on the Kerzman-Stein and the Neumann kernels for conformal mapping of doubly connected regions onto an annulus is presented. The theoretical development is based on the boundary integral equations for conformal mapping of doubly connected regions derived by Murid and Razali (1999). However, the integral equations are not in the form of Fredholm integral equation and no numerical experiments are reported. If some information on the zero and singularity of the mapping function is known, then the integral equations can be reduced to the numerically tractable Fredholm integral equations involving the unknown inner radius. For numerical experiments, discretizing the integral equations lead to a system of non-linear equations. The system obtained is solved simultaneously using Newton’s iterative method. Further modification of the integral equations of Murid and Razali (1999) has lead to an efficient and numerically tractable integral equations which involve the unknown inner radius. These integral equations are feasible for all doubly connected regions with smooth boundaries regardless of the information on the zeroes and singularities of the mapping functions. Discretizing the integral equations lead to an over determined system of non-linear equations which is solved using an optimization technique. Numerical implementations on some test regions are also presented.
format	Thesis
qualification_level	Master's degree
author	Mohamed, Nurul Akmal
author_facet	Mohamed, Nurul Akmal
author_sort	Mohamed, Nurul Akmal
title	An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
title_short	An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
title_full	An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
title_fullStr	An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
title_full_unstemmed	An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels
title_sort	integral equation method for conformal mapping of doubly connected regions via the kerzman-stein and the neumann kernels
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2007
url	http://eprints.utm.my/id/eprint/2153/1/NurulAkmalMohamedMFS20071.pdf
_version_	1747814403185573888

An integral equation method for conformal mapping of doubly connected regions via the Kerzman-Stein and the Neumann Kernels

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