A Trefftz/MFS mixed-type method to solve the Cauchy problem of the Laplace equation

被引：4

作者：

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

Wang, Fajie ^{[3
]}

Gu, Yan ^{[4
]}

机构：

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

[2] Natl Taiwan Ocean Univ, Ctr Excellence Ocean Engn, Dept Mech & Mechatron Engn, Keelung 20224, Taiwan

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

[4] Qingdao Univ, Coll Math, Qingdao 266071, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 87卷

关键词：

Laplace equation; Cauchy problem; Trefftz method; MFS test functions; Mixed-type method; BOUNDARY-ELEMENT METHOD; REGULARIZATION METHOD;

D O I：

10.1016/j.aml.2018.07.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By using the multiple-scale Trefftz method (MSTM) to solve the Cauchy problem of the Laplace equation in an arbitrary bounded domain, we may lose the accuracy several orders when the noise being imposed on the specified Cauchy data is quite large. In addition to the linear equations obtained from the MSTM, the fundamental solutions play as the test functions being inserted into a derived boundary integral equation. Therefore, after merely supplementing a few linear equations in the mixed-type method (MTM), which is a well organized combination of the Trefftz method and the method of fundamental solutions (MFS), we can improve the ill-conditioned behavior of the linear equations system and hence increase the accuracy of the solution for the Cauchy problem significantly, as explored by two numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：87 / 92

页数：6

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