A fast algorithm based on the domain decomposition method for scattering analysis of electrically large objects

By combining the finite difference (FD) method with the domain decomposition method (DDM), a fast and rigorous algorithm is presented in this paper for the scattering analysis of extremely large objects. Unlike conventional methods, such as the method of moments (MOM) and FD method, etc., the new algorithm decomposes an original large domain into small subdomains and chooses the most efficient method to solve the electromagnetic (EM) equations on each subdomain individually. Therefore the computational complexity and scale are substantially reduced. The iterative procedure of the algorithm and the implementation of virtual boundary conditions are discussed in detail. During scattering analysis of an electrically large cylinder, the conformal band computational domain along the circumference of the cylinder is decomposed into sections, which results in a series of band matrices with very narrow band. Compared with the traditional FD method, it decreases the consumption of computer memory and CPU time from O(N²) to O(N/m) and O(N), respectively, where m is the number of subdomains and N is the number of nodes or unknowns. Furthermore, this method can be easily applied for the analysis of arbitrary shaped cylinders because the subdomains can be divided into any possible form. On the other hand, increasing the number of subdomains will hardly increase the computing time, which makes it possible to analyze the EM scattering problems of extremely large cylinders only on a PC. The EM scattering by two-dimensional cylinders with maximum perimeter of 100,000 wavelengths is analyzed. Moreover, this method is very suitable for parallel computation, which can further promote the computational efficiency.