| In this dissertation, robust, efficient, and fast finite-element-based electromagnetic modeling is considered both for eigenvalue and force-excitation problems using enhanced formulations and algorithms. Complete hierarchical basis function spaces for the expansion of physical parameters in the finite element modeling are developed. Efficient and robust formulations and algorithms are presented for the two- and three-dimensional eigenvalue analysis. Finite-element-based model-order reduction algorithms are presented to build compact, broadband, and guaranteed-passive macromodels of electromagnetic devices for high-level simulation.; Multigrid and multilevel techniques are applied with the finite-element electromagnetic modeling to speed up the iterative solution of finite-element matrix equations. The smoothing operation in multigrid and multilevel techniques is performed on the vector and scalar potential formulation. Hybrid multilevel and multigrid techniques are combined in order to solve larger problems more accurately. The hybrid technique can be applied with hp-adaptive method.; Various numerical examples, including eigenvalue, scattering, and propagating problems, are solved to demonstrate the efficiency and robustness of our algorithms. Major contributions of the dissertation and future research for the full potential development of the method are discussed. |
