Due to the increasing complexity of geometric and material properties in electromagnetic models and applications, high-fidelity modeling and high-resolution computing present significant mathematical and computational challenges. The main objective of this research is to investigate high accuracy, high performance integral equation solvers for 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 that reduces the condition number of very large systems of equations. The strength and flexibility of the proposed method will be illustrated by means of several challenge real-world applications.