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Adaptive meshless methods for solvin...

Kwok, Ting On.

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Adaptive meshless methods for solving partial differential equations .

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Adaptive meshless methods for solving partial differential equations ./
作者:	Kwok, Ting On.
面頁冊數:	108 p.
附註:	Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1790.
Contained By:	Dissertation Abstracts International71-03B.
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3399571
ISBN:	9781109664775

Adaptive meshless methods for solving partial differential equations .
Kwok, Ting On.

Adaptive meshless methods for solving partial differential equations . - 108 p.

Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1790.

Thesis (Ph.D.)--Hong Kong Baptist University (Hong Kong), 2009.

RBF collocation method is one of the most popular meshless computational method and many applications of RBF collocation method in different areas can be found. In this thesis, we discuss the RBF collocation method for solving partial differential equations and related issues. Since some non-stationary problems can be treated as stationary problems after discretizing the time derivative, we consider the stationary problems first. We give the convergence proof of a least-squares asymmetric radial basis function collocation method for solving the modified Helmholtz equations which is the reduced problem of some nonstationary problems such as heat equation. Second, we propose a method to enhance the performance for solving 3D inhomogeneous elliptic equations. The above methods show the excellent performance if the solution is smooth enough. Third, instead of uniform nodes, refinement nodes are used if the solution contains sharp region. We show that using refinement nodes results in more accurate RBF approximation than uniform nodes if the solution contains high variations. Besides, the Hybrid RBF approach will be discussed for meshless interpolation and approximation. Lastly, we combine all developed methods to give an adaptive method for solving time-dependent partial differential equations. Some numerical examples of the heat and the Burger's equations will be given to conclude the work.

ISBN: 9781109664775Subjects--Topical Terms:

1669109
Applied Mathematics.

Adaptive meshless methods for solving partial differential equations .
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100 1 $a Kwok, Ting On. $3 1669402
245 1 0 $a Adaptive meshless methods for solving partial differential equations .
300 $a 108 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-03, Section: B, page: 1790.
500 $a Adviser: Leevan Ling.
502 $a Thesis (Ph.D.)--Hong Kong Baptist University (Hong Kong), 2009.
520 $a RBF collocation method is one of the most popular meshless computational method and many applications of RBF collocation method in different areas can be found. In this thesis, we discuss the RBF collocation method for solving partial differential equations and related issues. Since some non-stationary problems can be treated as stationary problems after discretizing the time derivative, we consider the stationary problems first. We give the convergence proof of a least-squares asymmetric radial basis function collocation method for solving the modified Helmholtz equations which is the reduced problem of some nonstationary problems such as heat equation. Second, we propose a method to enhance the performance for solving 3D inhomogeneous elliptic equations. The above methods show the excellent performance if the solution is smooth enough. Third, instead of uniform nodes, refinement nodes are used if the solution contains sharp region. We show that using refinement nodes results in more accurate RBF approximation than uniform nodes if the solution contains high variations. Besides, the Hybrid RBF approach will be discussed for meshless interpolation and approximation. Lastly, we combine all developed methods to give an adaptive method for solving time-dependent partial differential equations. Some numerical examples of the heat and the Burger's equations will be given to conclude the work.
590 $a School code: 0023.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Engineering, Mechanical. $3 783786
690 $a 0364
690 $a 0548
710 2 $a Hong Kong Baptist University (Hong Kong). $3 1020736
773 0 $t Dissertation Abstracts International $g 71-03B.
790 1 0 $a Ling, Leevan, $e advisor
790 $a 0023
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3399571