Interpreting and improving the PML absorbing boundary condition using anisotropic lossy mapping of space

The Berenger Perfectly Matched Layer (PML) absorbing boundary condition has been shown to be a remarkably effective means of terminating a computational grid for scattering simulations. By reinterpreting the PML equations as an anisotropic complex mapping of the normal coordinate, a compact frequency domain representation is derived, an error analysis is performed, and means for overcoming several deficiencies is presented. In particular, the problem of grazing incident waves can be minimized by increasing the real part of the mapping, altering the propagation direction to be more normal to the boundary. Also, finite difference, one-way wave equation PML terminations which further increase wave absorption are derived.