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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/42444

Title: Modified collocation Trefftz method for the geometry boundary identification problem of heat conduction
Authors: Chia-Ming Fan;Hsin-Fang Chan
Contributors: 國立臺灣海洋大學:河海工程學系
Date: 2011-01-28
Issue Date: 2017-05-12T08:17:22Z
Publisher: Numerical Heat Transfer, Part B: Fundamentals An International Journal of Computation and Methodology
Abstract: Abstract:In this article, a meshless numerical algorithm is proposed for the boundary identification problem of heat conduction, one kind of inverse problem. In the geometry boundary identification problem, the Cauchy data is given for part of the boundary. The Neumann boundary condition is given for the other portion of the boundary, whose spatial position is unknown. In order to stably solve the inverse problem, the modified collocation Trefftz method, a promising boundary-type meshless method, is adopted for discretizing this problem. Since the spatial position for part of the boundary is unknown, the numerical discretization results in a system of nonlinear algebraic equations (NAEs). Then, the exponentially convergent scalar homotopy algorithm (ECSHA) is used to efficiently obtain the convergent solution of the system of NAEs. The ECSHA is insensitive to the initial guess of the evolutionary process. In addition, the efficiency of the computation is greatly improved, since calculation of the inverse of the Jacobian matrix can be avoided. Four numerical examples are provided to validate the proposed meshless scheme. In addition, some factors that might influence the performance of the proposed scheme are examined through a series of numerical experiments. The stability of the proposed scheme can be proven by adding some noise to the boundary conditions.
Relation: 59(1), pp.58-75
URI: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/42444
Appears in Collections:[河海工程學系] 期刊論文

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