Applications of the perfectly matched layers in a discontinuous fluid media

In this thesis we study the applications of the PML in a multi-layered media. The PML is constructed for the scalar wave equation and the convergence and stability of the continuous problem is studied using the normal mode analysis. A high order accurate semi-discrete problem is constructed by approximating the spatial derivatives with high order finite difference operators satisfying the summation-by-parts properties. To have a stable semi-discrete approximation of the problem, we impose boundary conditions as well as interface conditions using the simultaneous approximation term technique. In order to gain accuracy, a transformed interface condition is constructed for the PML. The semi-discrete problem is approximated using second order accurate central difference scheme. To achieve higher order accuracy we modify the time marching scheme to eliminate truncation errors. Numerical experiments are presented showing that using the proposed transformed interface conditions, higher order of accuracy and convergence are achieved