An efficient integral equation method for electromagnetic and acoustic scattering simulations: convergence of multiple scattering iterations

One of the main difficulties in high-frequency electromagnetic and acoustic scattering simulations is that any numerical scheme based on the full-wave model entails the resolution of wavelength. It is due to this challange that simulations involving even very simple geometries are beyond the reach of classical numerical schemes.\\\\ In this talk, we shall present an analysis of a recently proposed integral equation method that bypasses the need for the resolution of wavelength, and thereby delivers solutions in frequency-independent computational times. Within single scattering configurations, the method is based on the use of an appropriate ansatz for the unknown surface densities and on suitable extensions of the method of stationary phase. The extension to multiple-scattering configurations, in turn, is attained through consideration of an iterative (Neumann) series that successively accounts for multiple reflections. We show that the convergence properties of this series in the high-frequency regime depends solely on geometrical characteristics. Moreover, for periodic orbits, we determine the convergence rate explicitly. Finally, we show that this insight suggests the use of alternative summation mechanisms that can greatly accelerate the convergence of the series.