TY - EJOU
AU - Ling, Leevan
AU - Takeuchi, Tomoya
TI - Boundary Control for Inverse Cauchy Problems of the Laplace Equations
T2 - Computer Modeling in Engineering \& Sciences
PY - 2008
VL - 29
IS - 1
SN - 1526-1506
AB - 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.
KW - Method of fundamental solution
KW - method of particular solution
KW - collocation method
KW - Tikhonov regularization
KW - L-curve
DO - 10.3970/cmes.2008.029.045