Generalized 3-D DSP-based FDTD algorithm for modelling the APML

Abstract

A generalized method for implementing the diagonal anisotropic perfectly matched layer (APML) in the finite difference time domain (FDTD) algorithm is presented for truncating three-dimensional (3-D) open region domains. The method is based on incorporating the digital signal processing algorithms developed for digital filters into the APML formulations. In this method, the permittivity and the permeability tensors of the APML are modelled as a set of infinite impulse response digital filters by using the Bilinear transformation technique. The proposed method has the advantage of the simplicity as it allows direct FDTD implementation of Maxwell's equations in the APML region and also can be used for modelling general FDTD domains such as lossy, dispersive, anisotropic, or nonlinear without any modifications. The new formulations are validated by analyzing 3-D radiation and guided-wave problems.