An interface-enriched generalized finite element method for the analysis and topology optimization of 2-D electromagnetic problems

有限元法 拓扑优化 拓扑(电路) 接口(物质) 扩展有限元法 数学 应用数学 计算机科学 数学优化 数学分析 物理 工程类 结构工程 机械 组合数学 气泡 最大气泡压力法
作者
Steven Bergen,Richard A. Norte,Alejandro M. Aragòn
出处
期刊:Computer Methods in Applied Mechanics and Engineering [Elsevier BV]
卷期号:421: 116748-116748 被引量:1
标识
DOI:10.1016/j.cma.2024.116748
摘要

The computational analysis of nanophotonic devices is usually carried out via the standard finite element method (FEM). However, FEM requires meshes that are fitted to the devices’ boundaries, so making changes to the geometry (and thus the mesh) results in an inefficient process at best. Such an approach is therefore at odds when conducting design, which requires the analysis of multiple device geometries until reaching a satisfactory solution. Computational design tools such as topology optimization are often used, but the use of density-based representations of geometry inevitably leads to other issues—e.g., pixelized fuzzy boundaries with “gray material” (that does not correspond to dielectric nor vacuum) have an adverse effect on the devices’ interaction with electromagnetic waves. In this paper we propose an interface-enriched generalized finite element method (IGFEM) for the analysis of two-dimensional electromagnetic scattering and eigenvalue problems. IGFEM enables the use of finite element meshes that are completely decoupled from the problem’s geometry. The analysis procedure is further coupled to a level set description of topology, resulting in a versatile enriched approach to topology optimization; this level set-based interface-enriched topology optimization procedure is devoid of the issues mentioned above regarding density-based methods, and yields crisp “black-and-white” designs that are devoid of jagged fuzzy edges. We first demonstrate that the analysis procedure achieves the same convergence rate as that of standard FEM using geometry-fitted meshes. We then compare the convergence properties of IGFEM with Nitsche’s method on a problem containing an embedded straight interface. Finally, we conduct topology optimization for designing both a 2-D metalens and a 2-D reflector, maximizing their ability to focus light onto a target point.
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