Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

被引：20

作者：

Chen, K. H. ^{[1
]}

Kao, J. H. ^{[2
]}

Chen, J. T. ^{[3
]}

Wu, K. L. ^{[4
]}

机构：

[1] Natl Ilan Univ, Dept Civil Engn, Ilan 26047, Taiwan

[2] Natl Cheng Kung Univ, Dept Hydraul & Ocean Engn, Tainan 70101, Taiwan

[3] Natl Taiwan Ocean Univ, Dept Harbor & River Engn, Chilung 20224, Taiwan

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

来源：

COMPUTATIONAL MECHANICS | 2009年 / 43卷 / 06期

关键词：

Desingularized meshless method; Tikhonov method; Truncated singular value decomposition method; Inverse problem; Subtracting and adding-back technique; ILL-POSED PROBLEMS; FUNDAMENTAL-SOLUTIONS; L-CURVE; TIKHONOV REGULARIZATION; NUMERICAL-SOLUTION; CAUCHY-PROBLEM; DOMAIN;

D O I：

10.1007/s00466-008-0348-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The desingularized meshless method (DMM) has been successfully used to solve boundary-value problems with specified boundary conditions (a direct problem) numerically. In this paper, the DMM is applied to deal with the problems with over-specified boundary conditions. The accompanied ill-posed problem in the inverse problem is remedied by using the Tikhonov regularization method and the truncated singular value decomposition method. The numerical evidences are given to verify the accuracy of the solutions after comparing with the results of analytical solutions through several numerical examples. The comparisons of results using Tikhonov method and truncated singular value decomposition method are also discussed in the examples.

引用

页码：827 / 837

页数：11

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