This work investigates the efficient and robust integral equation based solution of large multi-scale electromagnetic problems. The major technical ingredients in the proposed work include: (i) a scalable domain decomposition method for surface integral equations via a novel multi-trace formulation, (ii) a discontinuous Galerkin boundary element method, which employs discontinuous trial and testing functions without continuity requirements across element boundaries, and (iii) an optimized multiplicative Schwarz algorithm using complete second order transmission condition. The results obtained through this research greatly simplify the model preparation and mesh generation for complex electromagnetic simulation. Moreover, It provide an effective preconditioning scheme for the integral equation based solution of multi-scale problems. The strength and flexibility of the proposed method will be illustrated by means of several challenge real-world applications.