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
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Online Access:http://eprints.utm.my/id/eprint/78130/1/LeeKhiyWeiMFS2016.pdf
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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
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