The localized RBFs collocation methods for solving high dimensional PDEs

被引：50
作者：
Li, Ming [1 ]
Chen, Wen [2 ]
Chen, C. S. [1 ,3 ]
机构：
[1] Taiyuan Univ Technol, Sch Math, Taiyuan, Peoples R China
[2] Hohai Univ, Coll Mech & Mat, Nanjing, Jiangsu, Peoples R China
[3] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2013年 / 37卷 / 10期
基金：
中国国家自然科学基金;
关键词：
Localized RBF collocation method; Radial basis functions; Meshless methods; Method of approximate particular solutions; Kansa's method; APPROXIMATION;
D O I：
10.1016/j.enganabound.2013.06.001
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper we present a localized meshless method using radial basis functions (RBFs) for solving up to six dimensional problems. To improve the difficulty of selecting a shape parameter of RBF-MQ, a normalized scheme is introduced. We also make a comparison between the global and local RBF methods in terms of stability and accuracy. To demonstrate the applicability of the localized RBF method for high dimensional problems, two numerical examples with Dirichlet boundary conditions are given. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1300 / 1304
页数：5
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