Accurate, efficient, and stable domain decomposition methods for analysis of electromechanical problems

In this dissertation, advanced and robust numerical algorithms are developed to expand the capability and improve the efficiency of the finite-element analysis of electromechanical problems. First, the formulation of the dual-primal finite element tearing and interconnecting (FETI-DP) method is presented in details. With the FETI-DP method, an original large-scale problem is decomposed into smaller subdomain problems and parallel computing schemes are then employed to reduce the computation time significantly. Second, the tree-cotree splitting (TCS) method is adopted to deal with the low-frequency breakdown problem, which often accompanies the finite-element analysis of electromechanical problems. Third, higher-order hierarchical basis functions are implemented to improve the accuracy of the simulation and also to facilitate the treatment of the low-frequency breakdown problem. Fourth, the LU recombination method is adopted as an alternative for solving the low-frequency breakdown problem. Since the LU recombination method deals with the system matrices directly, it is a more general approach which can be applied across different basis functions or even different numerical methods. Various numerical examples are presented to validate the proposed algorithm and demonstrate its performance and applications