An FCC-FDTD Method on Nonuniform Grids With Guaranteed Stability for Electromagnetic Analysis

Abstract

The finite-difference time-domain (FDTD) method based on nonuniform face-centered cubic (FCC) grids, termed as NU-FCC-FDTD method, is proposed in this article. The FCC-FDTD method with uniform grids has a smaller numerical dispersion error than the traditional FDTD methods. To further enhance its efficiency and scalability, the NU-FCC-FDTD method is proposed to solve complex electromagnetic problems. Unlike the traditional FDTD methods based on Yee’s grids, for which the nonuniform grid technique is relatively straightforward, instability may occur when trying to apply nonuniform grids into the FCC-FDTD method. To ensure stability, cell-size-based correction factors are carefully defined in the time-marching formulations after taking cell sizes into consideration. Through comprehensive numerical dispersion analysis, the NU-FCC-FDTD method shows numerical dispersion advantage over the FDTD methods and the FCC-FDTD method with uniform grids. Furthermore, the stability condition is also given by using the parameter scanning method and verified in numerical examples. Four examples, including electromagnetic wave propagation, a dielectric rod (DR) resonator, a composite metallic-dielectric radome and the electromagnetic energy absorption of human head, are carried out to demonstrate its performance. Results show that the proposed NU-FCC-FDTD method can significantly improve efficiency compared with that of the FCC-FDTD method without compromising accuracy.