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

doi:10.3970/cmes.2008.030.065
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 30, No. 2, pp. 65-76, 2008
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Keywords Inverse problem, Modified Trefftz method, Biharmonic equation, Modified collocation Trefftz method (MCTM)
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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