Perfectly matched layer
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The perfectly matched layer (PML) approach to implementing absorbing boundary conditions in FDTD codes was proposed by Berenger in 1994 (see [1]). The approach involves surrounding the computational cell with a medium that in theory absorbs without any reflection electromagnetic waves at all frequencies and angles of incidence. Berenger showed that such a medium can be constructed as a lossy anisotropic dielectric with electric and magnetic conductivities of equal magnitude. (Of course, the magnetic conductivity requirement makes this an unphysical medium.)
The finite-difference implementation of PML requires the conductivities to be turned on gradually over a distance of a few grid points to avoid numerical reflections from the discontinuity.
