Higher-order FDTD algorithm using tetrahedral tessellation

The Yee-FDTD algorithm has dominated the field of electromagnetic simulation. While other competing techniques have significant advantages, they cannot compete with FDTD in terms of mathematical simplicity, and ease of implementation. Recently, Bossavit proposed the use of basis function defined on a tetrahedron and derived a Yee-like scheme. This scheme preserves the mathematical simplicity of Yee-like scheme and gives more freedom in modeling complex geometries. However, while the scheme is complete, several open questions remain. The foremost amongst them is the analysis of dispersion error. This paper explores the mathematical basis and numerical properties of this algorithm, and then extends it to a higher order scheme in space.