Choosing the right number of basis functions in multiscale transient simulation using Laguerre polynomials

Transient EM simulation using Laguerre polynomials is unconditionally stable and therefore, has the advantage of not being limited by any time-step. In the Laguerre method, the transient waveform of the field of interest is obtained by solving for a set of coefficients. These coefficients are used as weights and the weighted sum of Laguerre basis functions represents the time-domain waveform. This paper proposes a numerical solution to solve for the right number of basis coefficients in order to maximize the accuracy of the output transient waveform of interest. The method of choosing the right number of basis functions outlined in this paper is a key step for automation of the transient simulation technique using Laguerre polynomials.