Novel Algorithms for Ultra Scale Electromagnetic Problems in the Supercomputing Era

The need for increasing fidelity and accuracy in mission-critical electromagnetic applications have pushed the problem sizes toward extreme computational scales. Therefore, there is a large premium placed on the investigation of parallel and scalable integral equation simulators, a particularly useful class of computational electromagnetics, to meet this demand. This dissertation will focus on three interrelated areas: i) quasi-optimal, well-conditioned integral equation based domain decomposition methods, ii) geometry-adaptive, multi-scale discontinuous Galerkin boundary element methods, and iii) high-performance and scalable algorithms to reduce the computational complexity of extreme-scale simulations with the aid of parallel