The accuracy of temporal basis functions used in the TDIE method

A key parameter in the design of integral equation methods for transient electromagnetic scattering is the choice of temporal basis functions. Newly constructed basis functions have to meet requirements on accuracy, smoothness and efficiency, while the requirement of bandlimitedness is dropped for the nonlinear case. An analysis of the interpolation accuracy will justify the widespread use of the shifted Lagrange basis functions, because these have optimal accuracy, but introduce non-smoothness in the calculated fields. Alternatively, a novel spline basis function is proposed that has optimal accuracy under an additional smoothness constraint. Computational results confirm the expected smoothness and accuracy.