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We present a domain decomposition method as a preconditioner for Krylov-type solvers to model complex electromagnetic problems containing periodicities. The method reduces memory requirements by decomposing the original problem into several nonoverlapping sub-domains. The 1st order transmission condition is employed on interfaces between adjacent sub-domains to enforce continuity of electromagnetic fields and to ensure the sub-domain problems are well-posed. By following the spirit of duality paring a symmetric system is obtained. To reduce the computational burdens of the present method, the finite element tearing and interconnecting like algorithm is adopted. This algorithm results in the computation of the so-called "numerical" Green's function, which can be compressed efficiently via a rank-revealing matrix factorization algorithm. The final system matrix is solved by Krylov solvers instead of classical stationary solvers. To improve the convergence of iterative solvers, several robust implementation details are discussed and the choice of some popular Krylov-subspace solvers is studied through numerical examples.