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Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems

In this thesis, a new adaptive refinement coupled with variational multiscale element free Galerkin method (EFGM) is developed for solving high gradient problems. The aim of this thesis is to propose a new framework of moving least squares (MLS) approximation with coupling method based on the variat...

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Main Author: Liew, Siaw Ching
Format: Thesis
Language:English
Published: 2017
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/84133/1/LiewSiawChingPFS2017.pdf
http://eprints.utm.my/id/eprint/84133/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:126084
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spelling my.utm.841332019-12-16T01:56:28Z http://eprints.utm.my/id/eprint/84133/ Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems Liew, Siaw Ching QA Mathematics In this thesis, a new adaptive refinement coupled with variational multiscale element free Galerkin method (EFGM) is developed for solving high gradient problems. The aim of this thesis is to propose a new framework of moving least squares (MLS) approximation with coupling method based on the variational multiscale concept. Additional new nodes will be inserted automatically at high gradient regions by adaptive algorithm based on refinement criteria. An enrichment function is embedded in the MLS approximation for the fine scale part of the problem. Besides, this new technique will be parallelized by using OpenMP which is based on shared memory architecture. The proposed new approach is first applied in two-dimensional large localized gradient problem, transient heat conduction problem as well as Burgers' equation in order to analyze the accuracy of the proposed method and validated with an available analytic solutions. The obtained numerical results show a very good agreement with the analytic solutions and is able to obtain more accurate results than the standard EFGM. It is found that the average relative error of this new method is reduced in the range of 15% to 70%. Besides, this new method is also extended to solve two-dimensional sine-Gordon solitons. The results obtained show good agreement with the published results. Moreover, the parallelization of adaptive variational multiscale EFGM can improve the computational efficiency by reducing the execution time without loss of accuracy. Therefore, the capability and robustness of this new method has the potential to investigate more complicated problems in order to produce higher precision solutions with shorter computational time. 2017-04 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/84133/1/LiewSiawChingPFS2017.pdf Liew, Siaw Ching (2017) Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems. PhD thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:126084
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Liew, Siaw Ching
Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
description In this thesis, a new adaptive refinement coupled with variational multiscale element free Galerkin method (EFGM) is developed for solving high gradient problems. The aim of this thesis is to propose a new framework of moving least squares (MLS) approximation with coupling method based on the variational multiscale concept. Additional new nodes will be inserted automatically at high gradient regions by adaptive algorithm based on refinement criteria. An enrichment function is embedded in the MLS approximation for the fine scale part of the problem. Besides, this new technique will be parallelized by using OpenMP which is based on shared memory architecture. The proposed new approach is first applied in two-dimensional large localized gradient problem, transient heat conduction problem as well as Burgers' equation in order to analyze the accuracy of the proposed method and validated with an available analytic solutions. The obtained numerical results show a very good agreement with the analytic solutions and is able to obtain more accurate results than the standard EFGM. It is found that the average relative error of this new method is reduced in the range of 15% to 70%. Besides, this new method is also extended to solve two-dimensional sine-Gordon solitons. The results obtained show good agreement with the published results. Moreover, the parallelization of adaptive variational multiscale EFGM can improve the computational efficiency by reducing the execution time without loss of accuracy. Therefore, the capability and robustness of this new method has the potential to investigate more complicated problems in order to produce higher precision solutions with shorter computational time.
format Thesis
author Liew, Siaw Ching
author_facet Liew, Siaw Ching
author_sort Liew, Siaw Ching
title Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
title_short Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
title_full Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
title_fullStr Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
title_full_unstemmed Coupling of adaptive refinement with variational multiscale element free Galerkin method for high gradient problems
title_sort coupling of adaptive refinement with variational multiscale element free galerkin method for high gradient problems
publishDate 2017
url http://eprints.utm.my/id/eprint/84133/1/LiewSiawChingPFS2017.pdf
http://eprints.utm.my/id/eprint/84133/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:126084
_version_ 1654960045351239680
score 13.211869

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