Modified Convolutional Perfectly Matched Layers in the Presence of Moving Sources
Sameh Y. Elnaggar, Yahia M. M. Antar · 2024
In modern times, antennas are ubiquitous and interact in dynamic environments where they have the freedom to move in three-dimensional space. To accurately model the dynamic interactions, both frequency and time domain solvers are employed. The frequency domain solver computes fields before motion commences, while the time domain (transient) solver evolves the fields over time, accommodating the movements of antennas. The integration of both solvers becomes imperative, and in this context, we briefly delve into the necessary modifications required for the radiation boundary that models free (open) space. Our implementation incorporates Convolutional Perfectly Matched Layers (CPML), where electromagnetic fields interact with the CPML operator that is capable of effectively “absorbing” EM waves across a broad frequency spectrum and with arbitrary angles of incidence and polarizations. Traditional CPML methods assume null fields before time$t=0$; however, when initial fields are already present, such as the fields of antennas before$t=0$, their contribution should be included. This paper highlights the necessary modifications of CPML to encompass initial steady-state fields and demonstrates how the Finite Difference Time Domain (FDTD) update equations is modified by the inclusion of the initial components within the FDTD framework.