Boundary Control for Inverse Cauchy Problems of the Laplace Equations
Leevan Ling; and Tomoya Takeuchi

doi:10.3970/cmes.2008.029.045
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 29, No. 1, pp. 45-54, 2008
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Keywords Method of fundamental solution, method of particular solution, collocation method, Tikhonov regularization, L-curve.
Abstract The method of fundamental solutions is coupled with the boundary control technique to solve the Cauchy problems of the Laplace Equations. The main idea of the proposed method is to solve a sequence of direct problems instead of solving the inverse problem directly. In particular, we use a boundary control technique to obtain an approximation of the missing Dirichlet boundary data; the Tikhonov regularization technique and the L-curve method are employed to achieve such goal stably. Once the boundary data on the whole boundary are known, the numerical solution to the Cauchy problem can be obtained by solving a direct problem. Numerical examples are provided for verifications of the proposed method on the steady-state heat conduction problems.
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