Solving multi-scale electromagnetic problems by domain decomposition based integral equation method

In this paper, we introduced domain decomposition based integral equation (IE) methods for complicated multi-scale problems. The first multi-scale problem is solving electromagnetic scattering from a perfectly electric conductor with complicated geometry. A hybrid IE-DDM-MLFMA with Gauss-Seidel iteration is developed. As non-overlapping DDM, it has the advantage of flexible dividing domain and no buffer zone. The Gauss-Seidel iteration is proposed to update the currents on each sub-domain in real time, so the number of outer iterations is reduced greatly. The second multi-scale problem is electromagnetic analysis of large antenna array. To realize efficient solution, the tangential equivalence principle algorithm (T-EPA) combined with characteristic basis functions (CBFs) is presented. By utilizing the CBFs together with T-EPA, the analysis of large scale arrays will be more efficient with decreased unknowns compared with original T-EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the present methods.