Reaction–diffusion equation-based topology optimization code for electromagnetic wave problems using FreeFEM

In this paper, we present a structural topology optimization code for two-dimensional electromagnetic wave problems in the context of polarized electric field driven by the wave equation in the frequency domain for microwave range. The optimization process follows a phase field design approach, whic...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2021-12, Vol.64 (6), p.4367-4385
Main Authors: Jung, Mingook, Oh, Minkyu, Yoo, Jeonghoon
Format: Article
Language:English
Subjects:
Adaptive algorithms
Computational Mathematics and Numerical Analysis
Educational Paper
Electric fields
Electromagnetic radiation
Engineering
Engineering Design
Finite element method
Optimization
Reaction-diffusion equations
Source code
Theoretical and Applied Mechanics
Topology optimization
Wave equations
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Summary:In this paper, we present a structural topology optimization code for two-dimensional electromagnetic wave problems in the context of polarized electric field driven by the wave equation in the frequency domain for microwave range. The optimization process follows a phase field design approach, which is based on the reaction–diffusion equation combined with the double well potentials. In addition, a modified adaptive gradient algorithm is introduced for better performance and faster convergence rate. The salient features of the code are elaborated for the educational purpose; especially focused on the derivation of weak form in the finite element analysis for physical behavior simulation and the update of design variables. The corresponding code is written in the open-source software FreeFEM++, and it can be downloaded from the website http://ssd.yonsei.ac.kr .
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-021-03032-9