Stable non-orthogonal FDTD method

Abstract

Introduction: A number of techniques have been proposed to extend the classical Yee’s finite-difference time-domain (FDTD) algorithm to a grid that is conformal to curved objects. Such methods, including the nonorthogonal FDTD (NFDTD) [1, 2], can accurately represent the curved boundaries without resorting to inefficient staircase orthogonal meshes. However, their significant advantage is offset by the fact that they suffer from late time instabilities. In [3], it is demonstrated that the instability of NFDTD is inherent. Although a ‘time-subgriding’ approach is presented there to reduce the late time instability, an unconditionally stable NFDTD is still not obtained. In this Letter, we introduce a novel approach to discretise Maxwell’s equations using only the covariant components. It is demonstrated that the new NFDTD algorithm is stable over a very long period of numerical simulation. Moreover, the algorithm is less computationally intensive than other NFDTD methods [1, 2] where both of the covariant and contravariant components are needed. The proposed technique is validated by simulation results on a circular waveguide resonator.