Long-Time Instability Analysis of Pseudospectral Time-Domain Method

Lagrange polynomials-based Chebyshev pseudospectral time-domain (CPSTD) method uses Lagrange interpolation polynomials as basis functions to expand electromagnetic fields. Using the field values on all of the grids, Lagrange interpolation polynomials assure global calculation of spatial derivatives rather than local calculations. Because of this global approach, the method has spectral accuracy. Moreover, modeling of complex geometries is possible without introducing additional errors since the method is inherently conformal. Generally, the boundary conditions and multidomain patching are applied through characteristic variables (CVs) approach. However, the method suffers from long-time instability because of the boundary condition implementations. In this paper, the reasons for the instability of the method are analyzed and a stable solution for the cavity resonator simulation is proposed and verified.