Non-conformal domain decomposition methods for modeling EM problems with repetitions

Abstract

We proposed a non-conformal domain decomposition method (NC-DDM) for solving electromagnetic problems with significant repetitions: such as large finite antenna arrays, frequency selective surfaces, and metamaterials, to name just a few. To further improve the convergence in the DDM iterations, an optimal 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order transmission condition is introduced to enforce field continuities across domain interfaces. Moreover, many electromagnetic problems with repetitions are also electrically large. Consequently, the use of absorbing boundary condition may not be adequate as an accurate mesh truncation method. Herein, we combine directly the finite element domain decomposition method with a generalized combined field integral equation and form automatically the hybrid finite element and boundary integral (FEBI) method. The use of the boundary integral method, arguably, offers the best accuracy for modeling unbounded electromagnetic radiation and scattering problems, albeit at the increases of memory and CPU times. Furthermore, the finite element tearing and interconnecting (FETI) method is employed to take advantage of the repetitions to drastically reduce the computational resources.