Methods for improving finite-difference time-domain (FDTD) simulations of electromagnetic problems

In this dissertation, two methods for improving Finite-Difference Time-Domain (FDTD) simulations of electromagnetic problems are presented. It is divided into two main parts: one is stable subgridding schemes, and the other is the convolutional perfectly matched layers (CPML) derived by piecewise linear recursive convolution (PLRC) technique. First, the basic background of a subgridding scheme is discussed by introducing several existing prominent subgridding schemes. Based on the in-depth investigation into the essential factors composing a subgridding scheme, a standard uniform subgridding scheme with E -coupling is implemented assuring stability by symmetric coupling. Next, a novel graded sub-grid mesh is proposed to increase the stability margin. The graded sub-grid mesh combined with H -field coupling is verified to have a superior stability margin. For four different realistic electromagnetic problems, accuracy and efficiency estimations are carried out with respect to three implemented subgridding schemes. The numerical experiments prove that the proposed subgridding scheme yields improved simulation accuracy and efficiency. Moreover, the accuracy performance is enhanced further by using optimal interpolation methods without computational efficiency trade-off. For the second part of this dissertation, the CPML is reformulated using the PLRC method to improve absorption performance. The numerical reflection of the new piecewise-linear (PL) CPML is verified through a couple of experiments. The PL-CPML is shown to provide better reflection performance in both time-domain and frequency-domain evaluations than existing CPML in all of the numerical experiments. It is concluded that the improved accuracy compensates more than the slightly increased computational cost