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A local meshless collocation method for solving certain inverse problems
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DOI：10.1016/j.enganabound.2014.11.034.png)
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In this paper, we propose a meshless scheme based on compactly supported radial basis functions (CSRBFs) for solving the Cauchy problem of Poisson's equation and the inverse heat conduction problems in 2D. By assuming the unknown boundary condition to be a polynomial function, the inverse problems can be solved using a procedure similar to the process for solving forward problems. We employ Tikhonov regularization technique under L-curve regularization parameter to obtain a stable numerical solution. Numerical results verify the effectiveness and stability of this method. (C) 2014 Elsevier Ltd. All rights reserved.
Keyword:
Inverse problem
Compactly supported radial basis functions
Local meshless method
Tikhonov regularization
L-curve
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