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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myutmep.7813020180725T07:57:38Z Fast numerical conformal mapping of bounded multiply connected regions via integral equations 201612 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. 201612 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 
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Universiti Teknologi Malaysia 
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language 
English 
topic 
QA Mathematics 
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QA Mathematics Lee, Khiy Wei Fast numerical conformal mapping of bounded multiply connected regions via integral equations 
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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 