Spline-based high-order finite-difference time-domain (FDTD) schemes for the Maxwell equations

Abstract

In this paper, spline-based high-order FDTD schemes are developed to solve the Maxwell's equations with a bounded domain. In this scheme, all partial derivatives are approximated using cubic spline functions. This scheme uses the mesh stencil as used in the standard Yee cells and it is relatively easy to modify an existing code based on the Yee algorithm. This scheme can be adapted for an unbounded space problem such as a scatter in an unbounded space. In this case, the Maxwell's equations are transformed to a set of auxiliary equations in a closed domain. A reflection-free amplitude-reduction scheme applied over the entire computational domain reduces the auxiliary field components outwardly and makes them equal to zero at the closed boundary. Since the relationship between the physical fields and their auxiliary counterparts is explicity known and the former can be found from the latter with in the computational domain.