Nonlinear PML equations and their embedding into the FDTD framework

Since introduced by Berenger [1], the Perfectly Matched Layers (PML) has become a popular approach for non-reflecting Artificial Boundary Conditions (ABC) in the numerical solution of the time-dependent Maxwell equations on unbounded domains. All PML algorithms double the number of equations to be solved inside the artificial domain in Cartesian coordinates in 3D. Experimental observations and theoretical studies also show that in some cases the implementation of the PML leads to temporal growth of the reflections into the physical domain or (and) instabilities. In this work we present nonlinear PML equations which are strictly well posed, temporally stable, and do not require the solution of additional equations in the artificial domain. The combination of the nonlinear PML with the standard Yee algorithm allows its implementation into production codes without significant modifications. Numerical experiments show effectiveness of the nonlinear PML in both 2D and 3D simulations.