Inversion theory as applied to the optimisation of conductivity profile for PML absorbing boundary condition for FDTD code

A theoretical approach to obtain optimised profiles of the conductivity for the perfect matched layer (PML) absorbing boundary conditions is presented. The analytical expression recently introduced by the authors to estimate the error caused by the use of the PML backed by a metal plane as the absorbing boundary condition, has been minimised with respect to the conductivity profile following an inverse theory approach. The algorithm uses the Frechet derivative of the theoretical error expression, together with a simple regularisation technique in order to avoid the quasi-singularity intrinsic in the problem formulation. Results show that, following this approach, it is possible to easily obtain the conductivity profiles that render the performances of the absorbing boundary conditions comparable to, or better than, the best performance obtained for just a particular order of a more classic parabolic-like profile