A comparison between a spline-based method and a high-order FDTD scheme for the Maxwell equations

In this paper, two high-order FDTD schemes are developed to solve the Maxwell´s equations with a bounded domain. The first scheme is the extension of the standard Yee algorithms which rely on the approximation of a partial derivative by the central-difference approximation. The second scheme is based on a spline function. 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. Both schemes can be adapted for an unbounded space problem such as a scatter in an unbounded space.