Investigation of explicit finite-element time-domain methods and modeling of dispersive media and 3D high-speed circuits

In this dissertation, efficient time-domain domain decomposition algorithms are investigated, compared, and further enhanced, and a new domain decomposition method is proposed based on the knowledge of existing ones. First, several explicit domain decomposition methods, including the dual-field domain decomposition (DFDD) method and two versions of the discontinuous Galerkin time-domain (DGTD) method, are investigated and compared in terms of accuracy and efficiency. Furthermore, the hybrid versions of DFDD and DGTD are also compared. Second, the modeling of doubly lossy and dispersive media is incorporated into the DFDD method, which demonstrates the accuracy and efficiency in the comparative study, but can only model non-dispersive media in its original version. The phase error analysis indicates that the enhanced DFDD algorithm maintains the same accuracy level as the original version. Third, a new domain decomposition method named the layered domain decomposition (LADD) method is proposed. Based on the layered geometry of printed circuit board (PCB) structures, the unknowns within each subdomain are eliminated and a global interface problem containing only the unknowns at the via holes is obtained. The interface problem is then solved and the volume unknowns in each subdomain are recovered. This method maintains the unconditional stability of the finite element time-domain (FETD) method and generates results that are identical to FETD. Moreover, the algorithm is highly parallelizable since the computational time is dominated by the solution of subdomain problems which is performed independently for each subdomain. Various numerical examples are presented to compare the existing algorithms and to validate the proposed ones