Application of B-spline temporal basis function in time-domain finite element method for three-dimensional EM radiation problem

A new time-domain finite element method (TDFEM) based on B-spline temporal basis function is presented for the first time in this paper. This approach is motivated by aims of achieving higher computational efficiency. Compared with the reported TDFEM scheme, which is based on Galerldn’s method with a piecewise linear temporal expansion of electric field[t], in our scheme, the electric field is parameterised in terms of piecewise polynomial B-spline basis function. B-spline is chosen as temporal basis function both for a smoother interpolation and a more efficient approximation[2]. Moreover, this method 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 cavity problem, in which computed results agree with the analytical solution successfully. Then the scheme is applied to a bow-tie antenna and the results have good agreement with those in frequent-domain method.