A meshless generalized finite difference method for inverse Cauchy problems associated with three-dimensional inhomogeneous Helmholtz-type equations

被引：28

作者：

Hua, Qingsong ^{[1
]}

Gu, Yan ^{[2
]}

Qu, Wenzhen ^{[3
]}

Chen, Wen ^{[4
]}

Zhang, Chuanzeng ^{[5
]}

机构：

[1] Qingdao Univ, Sch Electromech Engn, Qingdao 266071, Peoples R China

[2] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Peoples R China

[3] Shandong Univ Technol, Sch Sci, Zibo 255049, Peoples R China

[4] Hohai Univ, Coll Mech & Mat, Nanjing 210098, Jiangsu, Peoples R China

[5] Univ Siegen, Dept Civil Engn, Paul Bonatz Str 9-11, D-57076 Siegen, Germany

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2017年 / 82卷

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Generalized finite difference method; Meshless method; Cauchy problem; Three-dimensional Helmholtz equation; Inverse problem; SINGULAR BOUNDARY METHOD; FUNDAMENTAL-SOLUTIONS; WAVE-PROPAGATION; MFS; ELASTICITY; RADIATION;

D O I：

10.1016/j.enganabound.2017.06.005

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. The method involves a coupling between the Taylor series expansions and weighted moving least-squares method. The main idea here is to fully inherit the high-accuracy advantage of the former and the stability and meshless attributes of the latter. This paper makes the first attempt to apply the method for the numerical solution of inverse Cauchy problems associated with three-dimensional (3D) Helmholtz-type equations. Numerical results for three benchmark examples involving Helmholtz and modified Helmholtz equations in both smooth and piecewise smooth 3D geometries have been analyzed. The convergence, accuracy and stability of the method with respect to increasing the number of scatted nodes inside the whole domain and decreasing the amount of noise added into the input data, respectively, have been well-studied. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：162 / 171

页数：10

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