Mesh-Splitting Impedance Transition Boundary Condition for Accurate Modeling of Thin Structures

Abstract

Numerical modeling of thin structures can result in dense volumetric discretization and poor mesh quality, which can be computationally expensive. A few equivalent boundary conditions are able to replace thin structures with zero-thickness surfaces and avoid volumetric discretization. However, their near-field solutions suffer from loss of accuracy as the thickness increases, because the reduction of thin structures to zero-thickness surfaces changes the original problem. This work presents a mesh-splitting technique for the impedance transition boundary condition (ITBC), which effectively eliminates the aforementioned error without additional number of unknowns. Under certain assumptions, the technique can be easily applied and yield much more accurate solutions than several other equivalent boundary conditions; otherwise, it may be unfeasible or lead to marginal improvements. Moreover, the mesh-splitting ITBC is incorporated into the spectral-element spectral-integral method for the modeling of doubly periodic problems including metasurfaces. Numerical examples include error analysis for the proposed technique and demonstrate its potential in more complex structures.