Ji-Chuan Liu1, Quan-Guo Zhang2
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 203-220, 2013, DOI:10.3970/cmes.2013.093.203
Abstract In this paper, we propose an algorithm to solve a Cauchy problem of the Laplace equation in doubly connected domains for 2D and 3D cases in which the Cauchy data are given on the outer boundary. We want to seek a solution in the form of the single-layer potential and discrete it by parametrization to yield an ill-conditioned system of algebraic equations. Then we apply the Tikhonov regularization method to solve this ill-posed problem and obtain a stable numerical solution. Based on the regularization parameter chosen suitably by GCV criterion, the proposed method can get the approximate temperature and heat… More >
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