Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys

In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to...

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Main Author:	Cheong, Hui Ting
Format:	Thesis
Language:	English
Published:	2017
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/80929/1/CheongHuiTingPFS2017.pdf
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spelling	my-utm-ep.809292019-07-24T00:10:52Z Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys 2017-06 Cheong, Hui Ting QA Mathematics In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to solve some examples of partial differential equations and the solutions obtained were compared with those obtained by MLDQ method in order to show the accuracy of the numerical method. The MLDQ method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain selected grid points. This present method together with the fourth-order Runge-Kutta (RK) method has been applied in differential equations such as wave equation and high gradient problems,. The MLDQ method can achieves accurate numerical solutions compared with FD method which is a low order numerical method by using a few number of grid points. The multiscale method was employed at the critical region which can break down the region of interest from coarser into finer grid points. Furthermore, FORTRAN programs were developed based on MLDQ method in solving some problems as above. The shared memory architecture of parallel computing was done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results show that the MLDQ method was a good numerical technique in two-dimensional SMA. 2017-06 Thesis http://eprints.utm.my/id/eprint/80929/ http://eprints.utm.my/id/eprint/80929/1/CheongHuiTingPFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:118686 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 Cheong, Hui Ting Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
description	In this research, the applicability of the Multiscale Localized Differential Quadrature (MLDQ) method in two-dimensional shape memory alloy (SMA) model was explored. The MLDQ method was governed in solving several partial differential equations. Besides, the finite difference (FD) method was used to solve some examples of partial differential equations and the solutions obtained were compared with those obtained by MLDQ method in order to show the accuracy of the numerical method. The MLDQ method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain selected grid points. This present method together with the fourth-order Runge-Kutta (RK) method has been applied in differential equations such as wave equation and high gradient problems,. The MLDQ method can achieves accurate numerical solutions compared with FD method which is a low order numerical method by using a few number of grid points. The multiscale method was employed at the critical region which can break down the region of interest from coarser into finer grid points. Furthermore, FORTRAN programs were developed based on MLDQ method in solving some problems as above. The shared memory architecture of parallel computing was done by using OpenMP in order to reduce the time taken in simulating the numerical results. Consequently, the results show that the MLDQ method was a good numerical technique in two-dimensional SMA.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Cheong, Hui Ting
author_facet	Cheong, Hui Ting
author_sort	Cheong, Hui Ting
title	Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
title_short	Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
title_full	Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
title_fullStr	Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
title_full_unstemmed	Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys
title_sort	multiscale localized differential quadrature in 2d partial differential equation for mechanics of shape memory alloys
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/80929/1/CheongHuiTingPFS2017.pdf
_version_	1747818281789554688

Multiscale localized differential quadrature in 2D partial differential equation for mechanics of shape memory alloys

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