TY  - EJOU
AU  - Liu, Ji-Chuan  
AU  - Zhang, Quan-Guo  

TI  - Cauchy Problem for the Laplace Equation in 2D and 3D Doubly Connected Domains
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2013
VL  - 93
IS  - 3
SN  - 1526-1506

AB  - 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 flux on the inner boundary. Numerical examples illustrate that the proposed method is reasonable and feasible.
KW  - Cauchy problem
KW  -  Laplace equation
KW  -  Integral equations
KW  -  Tikhonov regularization method
KW  -  GCV

DO  - 10.3970/cmes.2013.093.203