The perfectly matched layer (PML) constitutive tensors that match more general linear media presenting bianisotropic and dispersive behavior are obtained for single interface problems and for two-dimensional (2-D) and three-dimensional (3-D) corner regions. The derivation is based on the analytic continuation of Maxwell's equations to a complex variables domain. The formulation is Maxwellian so that it is equally applicable to the finite-difference time-domain (FDTD) or finite-element (FEM) methods. It recovers, as special cases, previous anisotropic media formulations, and dispersive media formulations.

No abstract

A simple and systematic derivation of anisotropic perfectly matched layers (PML's) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell's Equations to complex space. Through field transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrical and spherical systems is obtained, providing further clarification on the PML concept. As expected, these new PML media are cylindrically and spherically layered, respectively.Index Terms-Absorbing boundary conditions, anisotropic media, perfectly matched layer.

Abstract-

Perfectly matched layers (PML's) are derived for cylindrical and spherical finite-difference time-domain (FDTD) grids. The formulation relies on the complex coordinate stretching approach. Two-dimensional (2-D) cylindrical and three-dimensional (3-D) spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation by showing very good agreement between the perfectly matched layerfinite-difference time-domain (FDTD) results and the free-space analytic solutions.