This dissertation comprises the following four components. (1) Development of a robust and efficient 3-D finite element electromagnetic field solver with high-order vector elements for high-frequency and high-speed circuit simulations. The solver supports wave port and lumped port excitations as well as the incorporation of lumped networks and circuit models in a distributed finite element model. An adaptive multipoint model order reduction method is developed for fast broadband analysis. (2) Development of a fast and accurate multiconductor transmission line simulator and parameter extractor with improved model order reduction techniques. A methodology is further proposed for a combined quasi-TEM and full-wave transmission line analysis, which possesses their respective advantages and ensures full-wave accuracy from DC to very high frequencies. The transmission line analysis also takes into account the frequency dependence of dielectric materials. (3) Study of the low-frequency instability problem in the 3-D full-wave finite element simulation. The tree-cotree splitting is combined with several other techniques to improve the matrix conditioning and extend full-wave solutions down to very low frequencies for a more robust broadband characterization of high-speed digital circuits. (4) A combined domain decomposition–model order reduction (DD–MOR) method for efficient full-wave analysis of interconnections in multilayer printed circuit boards. The method not only brings a significant enhancement to computational efficiency while maintaining full-wave accuracy, but also provides great flexibility in the finite element mesh generation.
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