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A Spring-Damping Regularization and a Novel Lie-Group Integration Method for Nonlinear Inverse Cauchy Problems

Chein-Shan Liu1, Chung-Lun Kuo2
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan
Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, Taiwan. Corresponding author: E-mail: D96510001@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2011, 77(1), 57-80. https://doi.org/10.3970/cmes.2011.077.057

Abstract

In this paper, the solutions of inverse Cauchy problems for quasi-linear elliptic equations are resorted to an unusual mixed group-preserving scheme (MGPS). The bottom of a finite rectangle is imposed by overspecified boundary data, and we seek unknown data on the top side. The spring-damping regularization method (SDRM) is introduced by converting the governing equation into a new one, which includes a spring term and a damping term. The SDRM can further stabilize the inverse Cauchy problems, such that we can apply a direct numerical integration method to solve them by using the MGPS. Several numerical examples are examined to show that the SDRM+MGPS can overcome the ill-posed behavior of the inverse Cauchy problem. The present algorithm has good efficiency and stability against the disturbance from random noise, even with an intensity being large up to 10%, and the computational time is very saving.

Keywords

Inverse Cauchy problem, Quasi-linear elliptic equations, Spring-damping regularization method, Mixed group-preserving scheme

Cite This Article

Liu, C., Kuo, C. (2011). A Spring-Damping Regularization and a Novel Lie-Group Integration Method for Nonlinear Inverse Cauchy Problems. CMES-Computer Modeling in Engineering & Sciences, 77(1), 57–80.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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