A multiple-scale MQ-RBF for solving the inverse Cauchy problems in arbitrary plane domain

被引：20

作者：

Liu, Chein-Shan ^{[1
,2
]}

Chen, Wen ^{[1
,3
]}

Fu, Zhuojia ^{[1
,3
]}

机构：

[1] Hohai Univ, Coll Mech & Mat, Ctr Numer Simulat Software Engn & Sci, Nanjing 210098, Jiangsu, Peoples R China

[2] Natl Taiwan Univ, Dept Civil Engn, Taipei 10617, Taiwan

[3] Chinese Acad Sci, Inst Acoust, State Key Lab Acoust, Beijing 100190, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2016年 / 68卷

关键词：

Multiple-scale radial basis function expansion; Elliptic PDEs; Inverse Cauchy problem; Post-conditioner; COLLOCATION TREFFTZ METHOD; DATA APPROXIMATION SCHEME; CONDITION NUMBER; SHAPE PARAMETER; ERROR ESTIMATE; MULTIQUADRICS; EQUATIONS;

D O I：

10.1016/j.enganabound.2016.02.011

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The method of radial basis function (RBF) is popularly used in the solution of partial differential equations (PDEs). We propose a multiple-scale MQ-RBF method to solve the linear elliptic PDEs and the corresponding inverse Cauchy problems in simply- and doubly-connected domains, where the multiple scales are automatically determined a priori by the collocation points and source points, which play a role of post-conditioner of linear system to determine the unknown expansion coefficients. In the solution of inverse Cauchy problems the multiple-scale MQ-RBF is quite accurate and stable against large noise level up to 10-30%. Even for a case with only a quarter of boundary being imposed over-specified data, the multiple-scale MQ-RBF can still recover 75% unknown data very well. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：11 / 16

页数：6

共 22 条

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