A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

TLDR

The modified equations relate to the recently presented 2D perfectly matched layer and are of particular interest for FDTD computations on SIMD massively parallel supercomputers. The authors present a modified set of Maxwell's equations that incorporates complex coordinate stretching along the three Cartesian coordinates. The modified equations provide additional degrees of freedom that enable zero‑reflection absorbing boundaries at all angles and frequencies, and a 3D FDTD algorithm on a CM‑5 connection machine was developed to validate this approach. Simulation results confirm that the 3D FDTD algorithm achieves zero‑reflection absorbing boundaries across all angles and frequencies. © 1994 John Wiley & Sons, Inc.

Abstract

Abstract A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing‐material boundary conditions are of particular interest for finite‐difference time‐domain (FDTD) computations on a single‐instruction multiple‐data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM‐5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.