Numerical stability of nonorthogonalFDTD methods

In this paper, a sufficient test for the numerical stability of generalized grid finite-difference time-domain (FDTD) schemes is presented. It is show n that the projection operators of such schemes must be symmetric positive definite. Without this property, such schemes can exhibit late-time instabi lities. The origin and the characteristics of these late-time instabilities are also uncovered. Based on this study, nonorthogonal grid FDTD schemes ( NFDTD) and the generalized Yee (GY) methods are proposed that are numerical ly stable in the late time for quadrilateral prism elements, allowing these methods to be extended to problems requiring very long-time simulations. T he study of numerical stability that is presented is very general and can b e applied to most solutions.