Modeling Thin 3-D Material Surfaces Using a Spectral-Element Spectral- Integral Method With the Surface Current Boundary Condition

Thin dielectric or conductive structures are very common in many applications. Modeling such structures in the finite-element method can require a very dense mesh near the structures, which increases the computation cost and degrades the mesh quality. In this work, the surface current boundary condition is incorporated into the framework of the spectral-element spectral-integral method to efficiently model thin structures with double periodicity embedded in layered media. The thin structures are viewed as zero-thickness surfaces, and no dense mesh is required. Furthermore, a fast and convenient formulation is developed to evaluate the tangential field in the background of doubly periodic structures. Numerical experiments demonstrate the accuracy and efficiency of the proposed method by comparing with various reference solvers.

Automated summary

This paper proposes a method to efficiently simulate thin structures in the finite-element method. By incorporating the surface current boundary condition into the framework of the spectral-element spectral-integral method and treating the thin structures as zero-thickness surfaces, the need for a dense mesh is eliminated. Furthermore, a fast formulation is developed to evaluate the tangential field in the background of doubly periodic structures, improving the accuracy and efficiency of the computations.