Time Domain State Space Solver for Microwave Systems Based on Laguerre Polynomials

A time-domain state-space solver based on weighted Laguerre polynomials is presented. It is specifically designed for the design optimization of structures excited by predefined pulses. Applications include time-domain reflectometry, radar, and sonar. Such settings have in common that large numbers of systems are to be analyzed for the same excitation. The proposed method features offline-online decomposition, computes the Laguerre expansion of the system response at low cost, and facilitates its transformation to the frequency-domain. The algorithm is validated by a numerical example, involving dispersive material properties. Its performance is compared to that of a Runge-Kutta time-stepping method, with a focus on multi-query settings. A numerical example shows that the computation time of the new method is significantly faster than the Runge-Kutta method.