A Stabilized Marching-on-in-Degree Solution of Time Domain Combined Field Integral Equation

The instability problem of time domain integral equation (TDIE) remains one of the key obstacles to improve the quality of the TDIE solvers over the past decades. In this paper, the stabilized marching-on-in-degree (MOD) method of time-domain combined field integral equation (TD-CFIE-SMOD) is presented in solution of transient scattering problems. The instability problem of TDIE-MOD is primarily caused by the oscillatory nature of the Laguerre functions. Therefore, the Filon-type quadrature for excitation integrals and the Filon-type radial integration method on triangular domains is adopted in the TD-CFIE-SMOD solver. Some numerical results are presented to show the validity of the proposed solution of TD-CFIE using the current methodology.