A Transformation Media Based Approach for Efficient Monte Carlo Analysis of Scattering From Rough Surfaces With Objects

This paper presents a computational model that utilizes transformation-based metamaterials to enhance the performance of numerical modeling methods for achieving the statistical characterization of two-dimensional electromagnetic scattering from objects on or above one-dimensional rough sea surfaces. Monte Carlo simulation of the rough surface scattering problem by means of differential equation-based finite methods (such as finite element or finite difference methods) usually places a heavy burden on computational resources because at each realization of the Monte Carlo technique, a mesh must be generated anew for each surface realization. The main purpose of the proposed approach in this paper is to create a single mesh, without repeating mesh generation at each step, by introducing a transformation medium above the rough surface in the computational domain of the finite methods. Material parameters of the medium are obtained by the coordinate transformation technique, which is based on the form-invariance property of Maxwell´s equations. At each realization, only the material parameters are modified with respect to the geometry of surface without changing the mesh. In this manner, a great reduction in CPU time is achieved. The proposed technique is analyzed and validated via various finite element simulations.