Identification Of An Inner Boundary Of Laplace Equation

In this paper, we solve numerically an inverse problem of Laplace equation with the method of fundamental solutions (MFS). We consider a bounded simply-connected domain with smooth boundary such as D (?) Ω, and Ω\D is connected. First, the MFS is used to seek an approximation solution of the Laplace equation as a linear combination of fundamental solutions, whose the distinct singularities are distributed both inside the D and outside the Ω. Then we can write a non-linear function, which use the Cauchy boundary conditions on on (?)Ω and the third boundary condition on (?)D. Second, we discrete the objective function, based on the choices of singularities and boundary collocation points, and thus the problem of solving the Laplace equation of the inner boundary was turned to minimiz-ing the modified discreted function by optimization method. In the minimization process, we use the matlab optimization which is a comprehensive algorithm for finding an unconstrained nonlinear function. Finally, though numerical examples to verify the feasibility of the MFS of detecting the inner boundary problem of the Laplace equation.