A stable marching-on-in-time solver for time domain surface electric field integral equations based on exact integration technique

Theoretical studies and experience confirm that the stability of marching-on-in-time (MOT) solvers pertinent to the analysis of scattering from free-standing threedimensional perfect electrically conducting (PEC) surfaces hinges on the accurate evaluation of the MOT matrix elements resulting from a Galerkin discretization of the underlying integral equation. Unfortunately, accurate evaluation of the four-dimensional spatial integrals called for is prohibitively expensive when performed by numerical means. To mitigate this cost, two-dimensional integrals over source coordinates are evaluated analytically while the remaining two-dimensional integration over testing coordinates is carried out numerically; the technique assumes the use of Rao-Wilton-Glisson (RWG) spatial basis functions and Lagrange polynomial temporal expansions. While the MOT solver was shown to be stable for a wide range of problems involving up to 50,000 time steps, subsequent studies have revealed instabilities for small time steps.