Open Access

ARTICLE

The Spring-Damping Regularization Method and the Lie-Group Shooting Method for Inverse Cauchy Problems

by Chein-Shan Liu¹, Chung-Lun Kuo³, Dongjie Liu⁴

1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
2 Corresponding author. E-mail: liucs@ntu.edu.tw
3 Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Taiwan
4 Department of Mathematics, College of Sciences, Shanghai University, Shanghai, P. R. China

Computers, Materials & Continua 2011, 24(2), 105-124. https://doi.org/10.3970/cmc.2011.024.105

Abstract

The inverse Cauchy problems for elliptic equations, such as the Laplace equation, the Poisson equation, the Helmholtz equation and the modified Helmholtz equation, defined in annular domains are investigated. The outer boundary of the annulus is imposed by overspecified boundary data, and we seek unknown data on the inner boundary through the numerical solution by a spring-damping regularization method and its Lie-group shooting method (LGSM). Several numerical examples are examined to show that the LGSM can overcome the ill-posed behavior of inverse Cauchy problem against the disturbance from random noise, and the computational cost is very cheap.

---

Keywords

---