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.
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页码：11 / 16
页数：6
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