Monte Carlo simulations of Helmholtz scattering from randomly positioned array of scatterers by utilizing coordinate transformations in finite element method

Electromagnetic scattering from randomly distributed array of scatterers is numerically analyzed by Monte Carlo simulations by utilizing coordinate transformations in the context of finite element method solution of Helmholtz equation. The major goal in proposed approaches is to place transformation media into computational domain by employing the form invariance property of Maxwell's equations under coordinate transformations, and hence avoiding repeated mesh generation process in multiple realizations of the Monte Carlo method. A simple, single and uniform mesh is used, and only the material parameters of the transformation media are changed with respect to the positions of the objects in each realization. In this manner, computational resources are reduced considerably. The proposed approaches are demonstrated and compared with the standard approach via several numerical simulations. Monte Carlo results are presented in terms of some statistical properties (such as mean, standard deviation, probability density functions approximated by histograms) of radar cross section (RCS) and error values.