A low frequency stabilized convolution quadrature approach to electromagnetic scattering

The convolution quadrature (CQ) method of temporal discretization has several properties that make it an ideal method for the construction of marching-on-in-time schemes (Q. Chen, P. Monk, X. Wang, and D. S. Weile, Commun. Comput. Phys, 11, 383–399, 2012). In particular, the temporal discretization they yield is always renders accurate spatial integrations without any sharp shadow transition, and they can represent the Green´s functions in complicated, dispersive media with no special difficulty (X. Wang and D. S. Weile, IEEE Trans. Antenn. Propag., 59, 4651–4663, 2011). Finally, because of their close relationship with finite difference methods, they are ideal for the construction of boundary operators for FDTD (Y. Q. Lin and D. S. Weile, IEEE Trans. Antenn. Propag., 61, 2655–2663, 2014; S. Malevsky, E. Heyman, and R. Kastner, IEEE Trans. Antenn. Propag., 58, 3602-3609, 2010.)