Design of Temporal Basis Functions for Time Domain Integral Equation Methods With Predefined Accuracy and Smoothness

A key parameter in the design of integral equation methods for transient electromagnetic scattering is the definition of temporal basis functions. The choice of temporal basis functions has a profound impact on the efficiency and accuracy of the numerical scheme. This paper presents a framework for the design of temporal basis functions with predefined accuracy and varying smoothness properties. The well-known shifted Lagrange basis functions naturally fit in this framework. New spline basis functions will be derived that have the same interpolation accuracy as shifted Lagrange basis functions and with the added advantage of being smooth. Numerical experiments show the positive influence of smoothness on the quadrature error in the numerical integration procedure. The global accuracy in time of the numerical scheme based on shifted Lagrange and spline basis functions has been experimentally analyzed. For a given interpolation error the experiments confirm the expected accuracy for the shifted Lagrange basis functions, but remarkably show a higher order of accuracy for the spline basis functions.