Simulation of terrain propagation and diffraction using a 2D high-order accurate FMM-accelerated Nyström’s solver

A high-order accurate and efficient full-wave, 2D numerical algorithm is exploited to analyze electromagnetic waves propagating over irregular terrain. The algorithm derives its accuracy from the use of a locally corrected Nystrom scheme for discretizing the PMCHWT combined field integral equation, and its efficiency from the use of a fast multipole technique for speeding up the evaluation of far field interactions. The convergence rate of the solution is fully controllable, which renders the solver an attractive tool for simulating long-distance, over- terrain propagation and diffraction phenomena; for example, it is demonstrated that solutions with 8 digits of precision can be attained with as few as 8 surface discretization points per wavelength for a 1000-wavelength terrain profile.