Applying p-Step Lagrange Interpolation as Temporal Basis Functions to TDFEM for 3-D EM Radiation Problems

Accurate simulations of ultra-wideband (UWB) electromagnetic radiation from an antenna were developed based on a time-domain finite element method (TDFEM) based on p-step Lagrange interpolation for the temporal expansion. The motivation was to utilize the good interpolation features and straightforward computations for UWB antenna simulations. Numerical results were obtained from the cases of the cavity resonance problem, a bowtie and a Sierpinski bowtie antenna. Comparisons with an existing TDFEM approach employed linear temporal basis functions show good agreement to demonstrate the validity of the present schemes. The TDFEM with 2-step Lagrange interpolation as the temporal basis functions achieves better numerical results with only a small increase to run time and memory use in terms of the relative errors of the resonant frequency in the cavity for the transverse electric mode and the radiation patterns of the bowtie antenna.