A TDFEM-employed temporal second-order lagrange interpolation for three-dimensional EM radiation problems

This chapter investigates a new time-domain finite element method (TDFEM) based on Lagrange interpolation and high-order Whitney elements for temporal and spatial expansion, respectively. This approach is motivated by goals of achieving computational efficiency and further applying to ultra-wideband (UWB) antenna simulation. Traditional TDFEM scheme is based on Galerkin's method with a piecewise linear temporal expansion of the electric field. In this chapter, we use a second-order Lagrange interpolation polynomial instead of linear temporal expansion. Such a multistep interpolation scheme leads to a more robust interpolation and a more efficient approximation. Moreover, this method allows for a consistent time discretization of the electric field vector wave equation with the augmented perfectly matched layer (PML) regions. The novel scheme is first verified by applying on a canonical problem, i.e., the cavity resonance problem. The results achieved by this scheme were in close agreement with the analytical solution. We finally applied this scheme to a dipole antenna and compared the results from the TDFEM by using piecewise linear temporal basis function. We found that they were in good agreement with each other. ? Springer Science+Business Media, LLC 2010.EI