Fast numerical conformal mapping of bounded multiply connected regions via integral equations

This study presents a fast numerical conformal mapping of bounded multiply connected region onto a disk with circular slits, an annulus with circular slits, circular slits, parallel slits and radial slits regions and their inverses using integral equations with Neumann type kernel and adjoint genera...

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Main Author:	Lee, Khiy Wei
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/78130/1/LeeKhiyWeiMFS2016.pdf
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id	my-utm-ep.78130
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spelling	my-utm-ep.781302018-07-25T07:57:38Z Fast numerical conformal mapping of bounded multiply connected regions via integral equations 2016-12 Lee, Khiy Wei QA Mathematics This study presents a fast numerical conformal mapping of bounded multiply connected region onto a disk with circular slits, an annulus with circular slits, circular slits, parallel slits and radial slits regions and their inverses using integral equations with Neumann type kernel and adjoint generalized Neumann kernel. A graphical user interface is created to illustrate the effectiveness of the approach for computing the conformal maps of bounded multiply connected regions and image transformations via conformal mappings. Some image transformation results are shown via graphical user interface. This study also presents a fast numerical conformal mapping of bounded multiply connected region onto second, third and fourth categories of Koebe’s canonical slits regions using integral equations with adjoint generalized Neumann kernel. The integral equations are discretized using Nystr¨om method with trapezoidal rule. For regions with corners, the integral equations are discretized using Kress’s graded mesh quadrature. All the linear systems that arised are solved using generalized minimal residual method (GMRES) or least square iterative method powered by fast multipole method (FMM). The interior values of the mapping functions and their inverses are determined by using Cauchy integral formula. Some numerical examples are presented to illustrate the effectiveness for computing the conformal maps of bounded multiply connected regions. This study also discussed a fast numerical conformal mapping of bounded multiply connected regions onto fifth category of Koebe’s canonical regions using integral equations with the generalized Neumann kernel. An application of fast numerical conformal mapping to some coastal domains with many obstacles is also shown. 2016-12 Thesis http://eprints.utm.my/id/eprint/78130/ http://eprints.utm.my/id/eprint/78130/1/LeeKhiyWeiMFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:105135 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 Lee, Khiy Wei Fast numerical conformal mapping of bounded multiply connected regions via integral equations
description	This study presents a fast numerical conformal mapping of bounded multiply connected region onto a disk with circular slits, an annulus with circular slits, circular slits, parallel slits and radial slits regions and their inverses using integral equations with Neumann type kernel and adjoint generalized Neumann kernel. A graphical user interface is created to illustrate the effectiveness of the approach for computing the conformal maps of bounded multiply connected regions and image transformations via conformal mappings. Some image transformation results are shown via graphical user interface. This study also presents a fast numerical conformal mapping of bounded multiply connected region onto second, third and fourth categories of Koebe’s canonical slits regions using integral equations with adjoint generalized Neumann kernel. The integral equations are discretized using Nystr¨om method with trapezoidal rule. For regions with corners, the integral equations are discretized using Kress’s graded mesh quadrature. All the linear systems that arised are solved using generalized minimal residual method (GMRES) or least square iterative method powered by fast multipole method (FMM). The interior values of the mapping functions and their inverses are determined by using Cauchy integral formula. Some numerical examples are presented to illustrate the effectiveness for computing the conformal maps of bounded multiply connected regions. This study also discussed a fast numerical conformal mapping of bounded multiply connected regions onto fifth category of Koebe’s canonical regions using integral equations with the generalized Neumann kernel. An application of fast numerical conformal mapping to some coastal domains with many obstacles is also shown.
format	Thesis
qualification_level	Master's degree
author	Lee, Khiy Wei
author_facet	Lee, Khiy Wei
author_sort	Lee, Khiy Wei
title	Fast numerical conformal mapping of bounded multiply connected regions via integral equations
title_short	Fast numerical conformal mapping of bounded multiply connected regions via integral equations
title_full	Fast numerical conformal mapping of bounded multiply connected regions via integral equations
title_fullStr	Fast numerical conformal mapping of bounded multiply connected regions via integral equations
title_full_unstemmed	Fast numerical conformal mapping of bounded multiply connected regions via integral equations
title_sort	fast numerical conformal mapping of bounded multiply connected regions via integral equations
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2016
url	http://eprints.utm.my/id/eprint/78130/1/LeeKhiyWeiMFS2016.pdf
_version_	1747817914346504192

Fast numerical conformal mapping of bounded multiply connected regions via integral equations

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