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A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains

Chein-Shan Liu1

Department of Mechanical and Mechatronic Engineering, Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan. E-mail: csliu@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2008, 30(2), 65-76. https://doi.org/10.3970/cmes.2008.030.065

Abstract

Trefftz method (TM) is one of widely used meshless numerical methods in elliptic type boundary value problems, of which the approximate solution is expressed as a linear combination of T-complete bases, and the unknown coefficients are determined from boundary conditions by solving a linear equations system. However, the accuracy of TM is severely limited by its ill-conditioning. This paper is a continuation of the work of Liu (2007a). The collocation TM is modified and applied to the direct and inverse problems of biharmonic equation in a simply connected plane domain. Due to its well-conditioning of the resulting linear equations system, the present modified collocation Trefftz method (MCTM) can effectively solve the inverse problems without needing of overspecified data, iteration, and regularization. So that, the computational cost of MCTM is saving. Numerical examples show the effectiveness of the new method in providing highly accurate numerical solutions even subjecting to large noise of the given boundary data.

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Cite This Article

APA Style
Liu, C. (2008). A highly accurate MCTM for direct and inverse problems of biharmonic equation in arbitrary plane domains. Computer Modeling in Engineering & Sciences, 30(2), 65-76. https://doi.org/10.3970/cmes.2008.030.065
Vancouver Style
Liu C. A highly accurate MCTM for direct and inverse problems of biharmonic equation in arbitrary plane domains. Comput Model Eng Sci. 2008;30(2):65-76 https://doi.org/10.3970/cmes.2008.030.065
IEEE Style
C. Liu, "A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains," Comput. Model. Eng. Sci., vol. 30, no. 2, pp. 65-76. 2008. https://doi.org/10.3970/cmes.2008.030.065



cc Copyright © 2008 The Author(s). Published by Tech Science Press.
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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