This research concerns the use of domain decomposition methods for the integral equation based solution of large, complex electromagnetic problems. In particular, we investigate an effective coarse-graining approach via hierarchical skeletonization to address the computational challenges for multi-scale modeling and simulation. This work exploits the rank deficiency property exhibited in the interaction matrices between subdomains. We first employ the interpolative decomposition technique to select effective basis functions, the so-called skeletons, for individual subdomains. This skeletonization process is rigorous, error controllable, and can be achieved locally per subdomain and in parallel. Subsequently, the interactions between subdomains are computed using selected skeletons, and domain decomposition iterations are performed on the coarse-grained compressed system. Numerical results validate that the coarse-grained system exhibits a much smaller matrix dimension, provides desired confined eigenspectrum, and leads to a dramatic reduction in computational complexity for multi-scale problems of interest.