An FEM approach with FFT accelerated iterative robin boundary condition for electromagnetic scattering of a target with strong or weak coupled underlying randomly rough surface

To study electromagnetic scattering of a target above randomly rough surface, the Robin boundary condition (Robin BC) is employed to separate and enclose two isolate regions of the target and underlying surface. The fields in these two enclosed regions are strongly or weakly coupled by iteratively solving the scattering field integral equation in the finite element method (FEM) with updating the right-hand side residual of the Robin BC. This FEM approach presents an effective calculation for the model of the target at high altitude above large-scale rough surface to show their coupling interactions. Most time consuming of the algorithm is spent on evaluating the Robin BC on the fictitious planar boundary over the large-scale rough surface. The scattering field integral equation is written as the one-dimensional convolution form and is solved efficiently by using the fast Fourier transform (FFT). Our approach is first validated by available FEM-DDM (domain decomposition method) results. Then, the functional dependence of bistatic and back-scattering from the target above rough oceanic surface upon the target altitude, incident and scattering angle, etc., are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with strong or weak coupled interactions of a volumetric target at various altitudes above randomly rough surface.