Effective development of cylindrical finite-difference time-domain for electromagnetics applications

Abstract

Computationally, the size of the domain is important in terms of the memory and time to complete the run and collect the results. Thus, a conventional perfectly matched layer (PML) can be used to truncate computational regions in numerical methods. This will reduce the memory size and the time to complete the run. However, the accuracy of the PML is necessary in finite-difference time-domain (FDTD) method. It has been shown from past literature that for cylindrical FDTD (CFDTD) the accuracy of the PML is low especially near to the z-axis and for low frequency applications. Complex frequency shifted convolutional PML (CFS-PML) is a technique that is capable (when fully implemented) of absorbing evanescent waves by shifting the frequency poles in the imaginary axis. Such evanescent waves exist in cylindrical structures near the axis of rotation and need to be effectively absorbed if the CFDTD model is to be truncated within this region. Existing CFDTD PML implementations suffer from three drawbacks; first, they were restricted to downscaled CPML versions which only absorb propagating waves, not evanescent waves. Second, they all limited their PML performance analysis to rotationally invariant solution modes (zeroth mode). This is a critical omission as general wave solutions will exhibit a wide range of rotational modes that increasingly intensify and extend the reach of wave evanescence around the modeled structure’s axis of rotation. Third, existing CFDTD PML implementations share a common error of indiscriminately stretching all field components in the PML truncation region. This error is ineffectual when only rotationally invariant solutions are present. This is not the case, however, when other modes are present. This dissertation introduces a critical correction to the existing CFDTD PML to extend its validity beyond rotationally invariant wave solutions. Further, it will use the full version of CPML to include the necessary parameters to absorb evanescent waves. The end result is a CFDTD PML implementation, which can be placed in very close proximity to the axis of rotation, while still capable of absorbing strongly evanescent higher rotational solution modes. Such advancement will be critical for efficiently studying applications where the region of interest falls well within a single or even a fraction of wavelength from the axis of rotation.