Integral equation based on domain decomposition method for body of translation

In this paper, a hybrid scheme named IE-DDM-MLFMA with Gauss-Seidel iteration is proposed to calculate the scattering from the perfect electric conductor body of translation. The computational body of translation can be partitioned into concentric non-overlapping subdomains. Each of integral equation systems are solved separately, thus reducing the complexity of the original problem. For the solution of the resulting linear systems we describe appropriate iterative solution strategies using Gauss-Seidel iteration. A Local multilevel fast multipole algorithm is developed to further speed up the procedure of sweeping every interaction among sub-domains and this procedure is called outer iteration. Meanwhile, the iterative procedure in every periodic sub-domain called inner iteration is performed by MLFMA. It is available to applying two sets of MLFMA grids for the translation invariant feature of BOT problem. The main advantage offered by this technique is a reduction in memory requirement an.d CPU time. In addition block-diagonal pre-conditioner is utilized to speed up the convergence of iterative solutions. Numerical examples are presented that illustrate its potential.