Long-Time Instability of Pseudospectral Time-Domain Method in Curvilinear Coordinates

We found that the pseudospectral time-domain (PSTD) formulation discussed in the literature exhibits long-time instability when applied to problems with curvilinear geometry. To overcome this problem, we have developed a provably stable PSTD formulation in curvilinear coordinates. In this article, we discuss the new PSTD formulation and present a rigorous proof of stability. Numerical results are given to validate the new formulation. The new formulation requires only a simple change in the form of the spatial-derivative operators in curvilinear coordinates and so can easily be implemented in the existing PSTD codes.