Improved Forward Backward Method with Spectral Acceleration for scattering from exponentially correlated rough lossy surfaces

This paper presents an efficient and precise iterative method for computing the electromagnetic (EM) wave scattering from dielectric rough surfaces described by exponential correlation functions. The proposed method is based on improving the convergence rate of the Forward Backward Method (FBM) [1]. Moreover, a matrix splitting technique is introduced to reduce the number of matrix-vector multiplications required by the correction step and Spectral Acceleration (SA) [2], [3] is applied to reduce the computational complexity of each matrix-vector product from O(N²) to O(N). The proposed method is called the Improved Forward Backward Method with Spectral Acceleration (IFBM-SA) and is compared to FBM-SA in terms of convergence rate and the run time required to achieve a desired relative error norm. The numerical analysis demonstrates that IFBM-SA has a much higher convergence rate than FBM-SA. Therefore, IFBM-SA can be efficiently used to compute the electromagnetic scattering from randomly rough surfaces.