Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions

Many problems in science and engineering require the solution of the Dirichlet problem and Neumann problem with discontinuous coefficients. In this thesis, a boundary integral equation method is developed for solving Laplace’s equation with Dirichlet condition and Neumann condition with discontinuou...

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Main Author:	Aghaeibookheili, Mohsen
Format:	Thesis
Language:	English
Published:	2015
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/61060/1/MohsenAghaeiboorkheiliPFS2015.pdf
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id	my-utm-ep.61060
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spelling	my-utm-ep.610602017-03-13T04:23:48Z Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions 2015-03 Aghaeibookheili, Mohsen QA Mathematics Many problems in science and engineering require the solution of the Dirichlet problem and Neumann problem with discontinuous coefficients. In this thesis, a boundary integral equation method is developed for solving Laplace’s equation with Dirichlet condition and Neumann condition with discontinuous coefficients in both simply and multiply connected regions. The methods are based on a uniquely solvable boundary linear integral equation with the Neumann kernel. For numerical experiments, discretizing each integral equation leads to a system of linear equations. The system is then solved using the generalized minimum residual method (gmres) powered by the fast multipole method (FMM). After the boundary values of the solution of the Dirichlet problem and the Neumann problem with discontinuous coefficients in both simply and multiply connected regions are computed, the solution of the problem at the interior points are calculated by means of the Cauchy integral formula. The numerical examples presented have illustrated that the boundary integral equation methods developed yield high accuracy. Then a method by using these concepts is suggested for solving the mixed boundary value problem. The method is based on converting the mixed problem to a Riemann-Hilbert problem with discontinuous coefficients which is then reduced to two Dirichlet problems, one with discontinuous coefficients and one with unbounded coefficients. 2015-03 Thesis http://eprints.utm.my/id/eprint/61060/ http://eprints.utm.my/id/eprint/61060/1/MohsenAghaeiboorkheiliPFS2015.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:96353 phd doctoral 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 Aghaeibookheili, Mohsen Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
description	Many problems in science and engineering require the solution of the Dirichlet problem and Neumann problem with discontinuous coefficients. In this thesis, a boundary integral equation method is developed for solving Laplace’s equation with Dirichlet condition and Neumann condition with discontinuous coefficients in both simply and multiply connected regions. The methods are based on a uniquely solvable boundary linear integral equation with the Neumann kernel. For numerical experiments, discretizing each integral equation leads to a system of linear equations. The system is then solved using the generalized minimum residual method (gmres) powered by the fast multipole method (FMM). After the boundary values of the solution of the Dirichlet problem and the Neumann problem with discontinuous coefficients in both simply and multiply connected regions are computed, the solution of the problem at the interior points are calculated by means of the Cauchy integral formula. The numerical examples presented have illustrated that the boundary integral equation methods developed yield high accuracy. Then a method by using these concepts is suggested for solving the mixed boundary value problem. The method is based on converting the mixed problem to a Riemann-Hilbert problem with discontinuous coefficients which is then reduced to two Dirichlet problems, one with discontinuous coefficients and one with unbounded coefficients.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Aghaeibookheili, Mohsen
author_facet	Aghaeibookheili, Mohsen
author_sort	Aghaeibookheili, Mohsen
title	Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
title_short	Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
title_full	Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
title_fullStr	Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
title_full_unstemmed	Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
title_sort	solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2015
url	http://eprints.utm.my/id/eprint/61060/1/MohsenAghaeiboorkheiliPFS2015.pdf
_version_	1747817775870509056

Solving dirichlet and neumann problems with discontinuous coefficients on bounded simply and multiply connected regions

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