A Hybrid Finite Element Boundary Element Method for Periodic Structures on Non-Periodic Meshes Using Interior Penalty Method

摘要

Recent interests in analyzing/designing large finite arrays, frequency selective surfaces (FSS), and metamaterials speak volume of the need for a robust and efficient numerical method for arbitrary and inhomogeneous periodic structures in 3D. The development in general numerical methods for analyzing arbitrary 3-dimensional periodic structures is nothing new. Many existing literature ([1], [2], [3]) has thoroughly addressing this issue, including the hybridization of finite and boundary element method utilizes the Ewald transform to quickly compute the needed periodic Green's function. However, most of the work on modeling periodic structures relies on the availability of periodic meshes. Although such a constraint may not seem much a burden in many problem geometries, however, the relief of such a constraint still contributes greatly to the flexibility of applying the computer codes to periodic structures. This attribute has been the focus of a few recent publications on using non-periodic meshes for analyzing periodic structures. However, a hybridization of finite element and boundary element methods on non-periodic meshes has not been available yet, and that leads us to propose a possible solution to accomplish a successful hybridization without mesh constraint. To take into account non-periodic meshes, interior penalty approach [4] is utilized in this work to enforce proper periodic boundary conditions across non-matching side grids. Still, proper treatment in terms of boundary element part is required to address the non-conformity of the boundary element mesh. A more detailed description of the proposed method is presented in the following section.