Simulation of Near-Ground Long-Distance Radiowave Propagation Over Terrain Using NystrÖm Method With Phase Extraction Technique and FMM-Acceleration

A 2D surface integral equation-based NystrÖm solver in which a phase extraction technique is utilized to reduce the number of surface unknowns is described. As forward scattering is the dominant mechanism for the near-ground wave propagation scenario, the associated rapidly-varying phase components of the integral equation kernel and solution unknowns are deduced and isolated in advance and subsequently built into the solver. It is shown that by applying this method, when combining with an adaptive surface segmentation routine, as few as one to two average unknowns per wavelength is adequate in obtaining accurate solutions. This significantly reduces the memory storage and computational expense for the simulation of long-distance propagation effects. The efficiency of this method is further improved by incorporating it into the framework of the fast multipole scheme. The full details of the algorithm are discussed, along with performance comparisons of the new solver to a regular NystrÖm solver for terrain surfaces in terms of solution convergence.