Parallel fast multiple method for electromagnetic scattering from one-dimensional large-scale two-layered rough surfaces for large angles of incidence

A fast multiple method (FMM) is proposed for the fast implementation of electromagnetic scattering from one-dimensional (1-D) two-layered rough surfaces. Both horizontal (HH) and vertical (VV) polarised incident waves are considered. In particular, the focus in this study is on large angles of incidence. The parallel FMM is presented based on the message passing interface (MPI) of personal computer clusters. The bi-conjugate gradient method is adopted to solve the unsymmetrical matrix equation and is parallelised according to the property of MPI. The simulation time and parallel speedup ratio with different processors are also provided for one surface realisation. The algorithm is validated by comparing the angular distribution of bi-static scattering with that of the finite-difference time-domain (FDTD) technique. Bi-static scattering coefficient (BSC) by two-layered rough surfaces with different incident angles is exhibited. Finally, the influences of the characteristic parameters of rough surfaces, the relative permittivity of the media, as well as the average height between the two rough surfaces on the BSC for large angles of incidence are discussed.