Evaluation of stationary block iterative techniques for the solution of finite arrays using the fe-bi method and domain decomposition

In this paper, the finite element-boundary integral (FE-BI) method is used in the context of stationary iteration techniques to solve for the radiation patterns of linear and planar finite arrays of identical elements. The radiating element is a cavity-backed slot/patch (CBS/P) antenna which is decomposed into the interior region and the aperture region. The array elements are coupled to each other through the aperture unknowns and the free-space Green's function. The resulting block matrix system is solved using one of three stationary block iterative techniques namely the Jacobi method, the Gauss-Seidel (GS) method, and the successive over-relaxation (SOR) method. The rate of convergence and computational statistics of each of these block iterative techniques are examined and compared with each other.