An Oscillatory Quadrature Method for the Time-Domain Integral Equation using Laguerre Functions

The marching-on-in-degree (MOD) scheme which adopts the Laguerre functions as temporal basis functions, is one of the solutions of the time-domain integral equations (TDIE). It has been proved that the oscillatory integrals involving Laguerre functions may cause instability in the MOD method when marching on to a high degree. Therefore, a novel oscillatory quadrature method for Laguerre functions is proposed for stabilizing TDIE-MOD in this paper. The proposed oscillatory quadrature is applicable to the solution of time-domain magnetic field integral equations. Some numerical results of the transient scattering problem are given to show the effectiveness of the proposed oscillatory quadrature for the Laguerre functions in stable solution of TDIE.