Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Young, D. L.¹ 

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

关键词: Cauchy problem;    Inverse problem;    Laplace equation;    L-curve;    Method of fundamental solutions;    Singular point;    Tikhonov regularization;   

DOI  :  10.1016/j.jcp.2008.11.018

来源: Elsevier

【 摘 要 】

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularization parameter of the Tikhonov regularization technique and some parameters of the MFS. The L-curve determines a suitable regularization parameter for obtaining an accurate solution. Numerical experiments show that such a suitable regularization parameter coincides with the optimal one. Moreover, a better choice of the parameters of the MFS is numerically observed. It is noteworthy that a problem whose solution has singular points can successfully be solved. It is concluded that the numerical method proposed in this paper is effective for a problem with an irregular domain, singular points, and the Cauchy data with high noises. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free