Abstract: An asymptotic approximation method is proposed to solve a particular elliptic variational inequality of first kind associated with unilateral obstacle problems. In this method, the free boundary is first captured, and then the method of the fundamental solution (MFS) is used to find the solution of the Dirichlet problem for Laplace’s equation in the non-coincidence set. Numerical examples are given to show the efficiency of the method.

Key words: scattering, piezoelectric/piezomagnetic material, polarization method, dynamic Green's function, two-dimensional problem, Radon transform, anisotropic material, free boundary, variational inequality, obstacle problem, method of fundamental solution (MFS), asymptotic approximation method