On the stability of the FDTD algorithm for elastic media at a material interface

In this paper, the stability behavior of the first-order finite-difference time-domain algorithm for elastodynamics at the interface between two different materials is investigated. A necessary condition for stability is established, which, dependent on the material properties of the two media, might be more restrictive than the well-known Courant condition. It is shown that this more restrictive stability condition can be avoided if the material properties are averaged on the boundary.