Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions

This research is about computing the Green’s function for both bounded and unbounded multiply connected regions by using the method of boundary integral equation. The Green’s function can be expressed in terms of an unknown function that satisfies a Dirichlet problem. The Dirichlet problem is then s...

Full description

Saved in:

Bibliographic Details
Main Author:	Aspon, Siti Zulaiha
Format:	Thesis
Language:	English
Published:	2015
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/53533/25/SitiZulaihaAsponMFS2015.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.53533
record_format	uketd_dc
spelling	my-utm-ep.535332020-07-19T07:29:45Z Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions 2015-01 Aspon, Siti Zulaiha QA Mathematics This research is about computing the Green’s function for both bounded and unbounded multiply connected regions by using the method of boundary integral equation. The Green’s function can be expressed in terms of an unknown function that satisfies a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica software and MATLAB software plots of Green’s functions for several test regions for connectivity not more than three are also presented. For bounded regions with connectivity more than three and regions with corners, the linear system is solved iteratively by using the generalized minimal residual method (GMRES) powered by fast multipole method. This method helps speed up matrix-vector product for solving large linear system and gives both fast and accurate results. MATLAB software plots of Green’s functions for several test regions are also presented. 2015-01 Thesis http://eprints.utm.my/id/eprint/53533/ http://eprints.utm.my/id/eprint/53533/25/SitiZulaihaAsponMFS2015.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:84118 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 Aspon, Siti Zulaiha Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
description	This research is about computing the Green’s function for both bounded and unbounded multiply connected regions by using the method of boundary integral equation. The Green’s function can be expressed in terms of an unknown function that satisfies a Dirichlet problem. The Dirichlet problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with trapezoidal rule to discretize it to a linear system. The linear system is then solved by the Gauss elimination method. Mathematica software and MATLAB software plots of Green’s functions for several test regions for connectivity not more than three are also presented. For bounded regions with connectivity more than three and regions with corners, the linear system is solved iteratively by using the generalized minimal residual method (GMRES) powered by fast multipole method. This method helps speed up matrix-vector product for solving large linear system and gives both fast and accurate results. MATLAB software plots of Green’s functions for several test regions are also presented.
format	Thesis
qualification_level	Master's degree
author	Aspon, Siti Zulaiha
author_facet	Aspon, Siti Zulaiha
author_sort	Aspon, Siti Zulaiha
title	Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
title_short	Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
title_full	Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
title_fullStr	Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
title_full_unstemmed	Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions
title_sort	boundary integral equation with the generalized neumann kernel for computing green’s function for 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/53533/25/SitiZulaihaAsponMFS2015.pdf
_version_	1747817575154188288

Boundary integral equation with the generalized Neumann kernel for computing green’s function for multiply connected regions

Similar Items