This dissertation aims at developing sophisticated finite-element based numerical algorithms for efficient electromagnetic modeling and design of composite materials, fast frequency-domain scattering analysis of electrically large problems on massive parallelized computers, and efficient broadband analysis of resonant waveguide structures. To these ends, first, an interface-enriched generalized finite-element method (IGFEM) is introduced for electromagnetic analysis of heterogeneous materials. To avoid using conformal meshes, the method assigns generalized degrees of freedom at material interfaces to capture the discontinuities of the field and its derivatives, and maintains the same level of solution accuracy and computational complexity as the standard FEM based on conformal meshes. The fixed mesh nature combined with an analytical sensitivity analysis significantly reduces the computational cost in gradient-based shape optimization. Second, an efficient parallelization strategy is proposed for the domain decomposition based dual-primal finite-element tearing and interconnecting (FETI-DP) algorithm. Load balancing, global, neighboring, inter-processor communication minimization, and preconditioning techniques are adopted to improve the computational and parallel efficiency. An inhomogeneous truncation boundary condition is presented to enable the FETI-DP simulation of a stratified medium. The parallel FETI-DP algorithm is also combined with a fast near- to far-field transformation and a linear interpolation technique for efficient vectorial field imaging of electrically large objects. Finally, a hybrid technique that consists of the time- and frequency-domain computations and model-order reduction strategy is developed for the efficient simulations of resonant waveguide structures. Numerous results are presented to demonstrate the accuracy, efficiency, and capability of the proposed methods
