Novel approach to construct temporal basis functions for time-domain integral equation method

Time-domain integral equation (TDIE) methods, for the solution of transient electromagnetic problems have steadily increased in popularity. A novel construction method is presented to design the new temporal basis function. We first specify the principal properties of the desirable temporal basis function. According to these properties and choosing a suitable function with some parameters, we construct a nonlinear programming problem with respect to these parameters, from which the new temporal basis function can be derived. The obtained temporal function has the any-order continuous derivative and is not a truncated version of any function. By using the construction method, a new temporal function, namely, the rational fractional temporal function, is also presented. The numerical result shows that the new temporal function pushes the occurrence of the late-time instability of the transient simulation further down in time when compared to the previous temporal functions.