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

Mingook Jung, Minkyu Oh, Jeonghoon Yoo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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

Original languageEnglish
Pages (from-to)4367-4385
Number of pages19
JournalStructural and Multidisciplinary Optimization
Issue number6
Publication statusPublished - 2021 Dec

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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