Two-dimensional transverse-magnetic time-domain scattering using the Nyström method and Green´s function filtering

Time-domain integral equations are uniquely suited to modeling many electromagnetic scattering phenomena, such as broadband, nonlinear, and time-varying problems. While a method of moments-like Galerkin approach is usually used in their discretization, in principle, the locally corrected Nyström method is equally applicable. The Nyström method has several advantages over Galerkin´s method. It only requires the evaluation of the Green´s function to compute most matrix elements so the setup phase requires less computation, and complex, multipatch parametric basis functions are completely avoided (Canino, L.F. et al., J. Computational Phys., vol.146, p.627-63, 1998). For a time-domain formulation, the spatial integration rules are unchanged; however, the Green´s function is not bandlimited, so any temporal sampling results in aliasing. Also, the local corrections approach outlined by Canino et al. accounts for the spatial singularity of the Green´s function, but not the temporal singularity. These problems are intimately linked and can be addressed by filtering the Green´s function, resulting in an accurate and stable method.