A Novel Subdomain 2D/Q-2D Finite Element Method for Power/Ground Plate-Pair Analysis

Abstract

Upon excitation by a surface magnetic current, a power/ground plate-pair supports only $\mathrm{TM}^{z}$ modes. This means that the magnetic field has only azimuthal components permitting a simple but effective domain decomposition method (DDM) to be used. In the proximity of an antipad, field interactions are rigorously modeled by a quasi-two-dimensional (Q-2D) finite element method (FEM) making use of three-dimensional (3D) triangular prism mesh elements. Since high-order $\mathrm{TM}^{z}$ modes are confined in the close proximity of the antipad, field interactions in the region away from the antipad only involve the fundamental mode and are rigorously modeled by a 2D FEM. This approach reduces 3D computation domain into a hybrid 2D/Q-2D domain. The discretization of this hybrid domain results in a global matrix system consisting of two globally coupled matrix equations pertinent to 2D and Q-2D domains. In this article, these two matrix equations are “decoupled” using a Riemann solver and the information exchange between the two domains is facilitated using numerical flux. The resulting decoupled two matrix equations are iteratively solved using the Gauss–Seidel algorithm. The accuracy, efficiency, and robustness of the proposed DDM are verified by four representative examples.