TY  - EJOU
AU  - Chi, h-Chang 
AU  - Yeih, Weichung  
AU  - Liu, Chein-Shan  

TI  - A Novel Method for Solving the Cauchy Problem of Laplace Equation Using the Fictitious Time Integration Method
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2009
VL  - 47
IS  - 2
SN  - 1526-1506

AB  - In this study, a novel method for solving the Cauchy problem of Laplace equation is developed. Through the fictitious time integration method (FTIM), the finding of the root of the resulting linear equations can be transformed into for finding the fixed point of a system of first order ordinary differential equations, in which a fictitious time variable is introduced. In such a sense, the inverse of ill-posed leading matrix is not necessary for the FTIM. This method uses the residual of each equation to control the evolution of unknowns in the fictitious time, and it is different from the conventional iteration method where an artificial iteration rule is required. Comparing to the Tikhonov's regularization method, the FTIM does not need to seek for the optimal regularization parameter, and it also needs not to seek for the inverse of the leading coefficient matrix in each step. Numerical results are given to show the validity of the current approach and it can be seen that this method can obtain reasonable results with or without noise. It shows a better noise resistance than the Tikhonov's regularization method.
KW  - Inverse Cauchy problem
KW  -  Laplace equation
KW  -  Boundary element method
KW  -  Fictitious Time Integration Method
KW  -  Tikhonov's regularization method

DO  - 10.3970/cmes.2009.047.167