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 10 条

[1] An energy regularization of the MQ-RBF method for solving the Cauchy problems of diffusion-convection-reaction equations
Liu, Chein-Shan
Chang, Chih-Wen
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2019, 67 : 375 - 390
[2] A multiple-scale Pascal polynomial triangle solving elliptic equations and inverse Cauchy problems
Liu, Chein-Shan
Kuo, Chung-Lun
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2016, 62 : 35 - 43
[3] A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems
Liu, Chein-Shan
Young, D. L.
JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 312 : 1 - 13
[4] The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems
Liu, Chein-Shan
Kuo, Chung-Lun
Jhao, Wun-Sin
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2016, 95 : 936 - 943
[5] Boundary value identification of inverse Cauchy problems in arbitrary plane domain through meshless radial point Hermite interpolation
Youssef El Seblani
Elyas Shivanian
Engineering with Computers, 2020, 36 : 1155 - 1168
[6] Boundary value identification of inverse Cauchy problems in arbitrary plane domain through meshless radial point Hermite interpolation
El Seblani, Youssef
Shivanian, Elyas
ENGINEERING WITH COMPUTERS, 2020, 36 (03) : 1155 - 1168
[7] A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains
Liu, Chein-Shan
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2008, 35 (02): : 91 - 111
[8] Fast Solving the Cauchy Problems of Poisson Equation in an Arbitrary Three-Dimensional Domain
Liu, Cheinshan
Wang, Fajie
Qu, Wenzheng
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2018, 114 (03): : 351 - 380
[9] A novel Trefftz method for solving the multi-dimensional direct and Cauchy problems of Laplace equation in an arbitrary domain
Lin, Ji
Liu, Chein-Shan
Chen, Wen
Sun, Linlin
JOURNAL OF COMPUTATIONAL SCIENCE, 2018, 25 : 16 - 27
[10] On Solving Three-dimensional Laplacian Problems in a Multiply Connected Domain Using the Multiple Scale Trefftz Method
Ku, Cheng-Yu
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2014, 98 (05): : 509 - 541

← 1 →