A 2D/Q-2D Subdomain Finite Element Method for Irregular Power/Ground Plate-Pair Analysis with Waveport Excitation

The field distribution of a power/ground plane can be fully characterized by TM
zmn
modes, where the electric fields have both azimuthal and longitudinal components and the magnetic fields have only the azimuthal component. Thus, if the magnetic fields are defined to be the unknowns in the finite element method (FEM) used for the analysis of the power/ground plane structure, the analysis becomes a quasi-two dimensional (Q-2D) problem. Since the high-order modes are evanescent, they are tightly confined to the near region of the vias guarded by anti-pads; while in the regions sufficiently far from the anti-pads, only the fundamental mode should be accounted for. Therefore, the Q-2D problem is naturally transformed to be a hybrid 2D and Q-2D one. Compared with the brute-force three dimensional (3D) analysis, the number of unknowns is significantly reduced. To further reduce the computational cost, a new Riemann solver inspired domain decomposition method (D-DM), which accounts for the 2D and Q-2D region separately, is further proposed. The numerical flux for the Maxwell equations are used to realize the information exchange between the two domains. Finally, numerical examples are given to verify the proposed method.