An anisotropic perfectly matched layer-absorbing medium in finite element time domain method for Maxwell´s equations

When we try to solve Maxwell´s equations by a numerical method like the finite difference or finite element, one of the major question is: how to close the calculus domain? This is a mathematical question. Another point of view is: how to simulate an anechoic chamber in order not to be disturbed by reflections of the waves. The first way to answer this question was to use absorbing boundary conditions. Sacks et al. (see IEEE Trans. Antenna Propag., vol.43, no.l2, p.1460-3, 1995) present an approach for deriving a perfectly matched layer (PML) for mesh truncation. This approach is based on using anisotropic material properties to describe the absorbing layer. They have shown that the material properties of the medium can be chosen such that a planar interface between the anisotropic medium and free-space is perfectly reflectionless. This approach offers the advantage that it does not require a modification of Maxwell´s equations and it is very easy to implement in finite elements. Sacks et al. present a formulation in frequency domain. We present the use of this approach in the finite element time domain.