Optimizing Level Set–Based Topology Optimization: Application to 2D Electromagnetic Problems
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Topology optimization is increasingly being adopted for designing optical components such as met-alenses, where smooth, well-resolved material interfaces strongly influence wave-propagation performance. A recent approach combines a level set description of topology—parameterized via radial basis functions (RBFs)—and enriched finite element analysis (e-FEA) [1, 2]. In particular, for enriched analysis we use the Interface-enriched Generalized Finite Element Method (IGFEM) [3], which enables smooth material edges without remeshing by enhancing the approximation space with enrichment functions that capture the kinematics of material (weak) discontinuities. However, our first optimization procedure often exhibited oscillations in the objective function that were poorly understood. In this study, we systematically investigate how key parameters—RBF radii, design and simulation mesh sizes, initial level set hole seeding, enriched-node placement strategies, level-set regularization, and optimizer settings—affect stability and final performance. Using a set of benchmark tests (simulation accuracy, shape-matching optimization, and electromagnetic identification optimization), we show that while large RBF radii can represent fine geometric features, this capability does not reliably carry over during optimization, and overfitted initial design fields can trigger oscillatory behavior. We then apply the tuned formulation to a metalens design for improving scintillator light-collection efficiency. With default parameters, the optimization is highly sensitive to RBF settings and exhibits strong objective oscillations; with optimized parameters, oscillations are suppressed up to convergence and the final design performance improves by 12%. REFERENCES [1] S. J. van den Boom, J. Zhang, F. van Keulen, and A. M. Aragón. An interface-enriched generalized finite element method for level set-based topology optimization. Struct Multidiscip O, 63(1):1–20, 2020. [2] Steven van Bergen, Richard A. Norte, and Alejandro M. Aragón. An interface-enriched generalized finite element method for the analysis and topology optimization of 2-D electromagnetic problems. Comput Methods Appl Mech Eng, 421, 3 2024. [3] Alejandro M. Aragón, Bowen Liang, Hossein Ahmadian, and Soheil Soghrati. On the stability and interpolating properties of the hierarchical interface-enriched finite element method. Comput Methods Appl Mech Eng, 362:112671, 2020.
