Time-domain finite element method based on Smoothed Cosine temporal basis function for three-dimensional EM radiation problem

A novel time-domain finite element method (TDFEM) based on smoothed cosine temporal basis function is presented in this paper. This method is motivated by goals of achieving higher computational efficiency. Unlike the reported TDFEM scheme[Z. Lou and J. Jin, 2005], which is based on Galerkin´s method with a piecewise linear temporal expansion of electric field, the electric field in our approach is expanded in terms of smoothed cosine basis function. Smoothed cosine function is chosen as temporal basis function for not only a smoother interpolation but also a more robust approximation [A. Taflove, 1995]. Moreover, this scheme allows for a consistent time discretization of the electric field vector wave equation and its augmented PML regions. The novel scheme is first verified on a cavity problem, whose results agree with the analytical solution very well. Finally the scheme is applied to a dipole antenna and the results have good agreement with those from TDFEM based on linear temporal basis function.