A Meshless Method for Solving Nonhomogeneous Cauchy Problems
作者： Ming Li , C.S. Chen , Y.C. Hon
DOI: 10.1016/J.ENGANABOUND.2010.09.003
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摘要: In this paper the method of fundamental solutions (MFS) and particular solution (MPS) are combined as a one-stage approach to solve Cauchy problem for Poisson's equation. The main idea is approximate equation using linear combination radial basis functions. As result, we provide direct effective meshless solving inverse problems with inhomogeneous terms. Numerical results in 2D 3D show that our proposed problems.
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Y.C. Hon, T. Wei, The method of fundamental solution for solving multidimensional inverse heat conduction problems Cmes-computer Modeling in Engineering & Sciences. ,vol. 7, pp. 119- 132 ,(2005) , 10.3970/CMES.2005.007.119
A.L. Bukhgeim, J. Cheng, M. Yamamoto, Uniqueness and stability for an inverse problem of determining a part of boundary Inverse Problems in Engineering Mechanics. pp. 327- 336 ,(1998) , 10.1016/B978-008043319-6/50038-8
Graeme Fairweather, Andreas Karageorghis, The method of fundamental solutions for elliptic boundary value problems Advances in Computational Mathematics. ,vol. 9, pp. 69- 95 ,(1998) , 10.1023/A:1018981221740
Michael A. Golberg, Boundary integral methods : numerical and mathematical aspects Computational Mechanics Publications/WIT Press. ,(1999)
Liviu Marin, The Method of Fundamental Solutions for Inverse Problems Associated with the Steady-State Heat Conduction in the Presence of Sources Cmes-computer Modeling in Engineering & Sciences. ,vol. 30, pp. 99- 122 ,(2008) , 10.3970/CMES.2008.030.099
Liviu Marin, Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data Cmes-computer Modeling in Engineering & Sciences. ,vol. 37, pp. 203- 242 ,(2008) , 10.3970/CMES.2008.037.203
Y C Hon, T Wei, Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation Inverse Problems. ,vol. 17, pp. 261- 271 ,(2001) , 10.1088/0266-5611/17/2/306
Takemi Shigeta, D.L. Young, Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points Journal of Computational Physics. ,vol. 228, pp. 1903- 1915 ,(2009) , 10.1016/J.JCP.2008.11.018
Hui Wang, Qing-Hua Qin, A meshless method for generalized linear or nonlinear Poisson-type problems Engineering Analysis With Boundary Elements. ,vol. 30, pp. 515- 521 ,(2006) , 10.1016/J.ENGANABOUND.2006.01.009
Rudolf Mathon, R. L. Johnston, The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions SIAM Journal on Numerical Analysis. ,vol. 14, pp. 638- 650 ,(1977) , 10.1137/0714043