A multi-objective topology optimisation for 2D electro-magnetic wave problems with the level set method and BEM

Hiroshi Isakari, Kenta Nakamoto, Tatsuya Kitabayashi, Toru Takahashi, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We have been investigating applications of a level set-based topology optimisation for wave devices with the boundary element method. For two-dimensional electro-magnetic wave problems, we have, so far, proposed a topology optimisation which can find a configuration of dielectric materials to locally minimise an objective functional such as the intensity of transverse electric (TE) or transverse magnetic (TM) polarised wave with a specific frequency. As an extension of our methodology, this paper presents a multi-objective topology optimisation, which can deal with some objective functionals simultaneously. The present method, for instance, can find a material distribution which can locally minimise the intensity of both TM and TE waves with multiple frequencies. The basic idea of the proposed method is to use the weighted sum or the Kreisselmeier–Steinhause function of the original objective functionals as a new objective functional. We present a derivation of the topological derivative for the new objective functional, and a detailed algorithm of the optimisation process with the derived topological derivative. We also present some numerical examples to illustrate the validity and efficiency of the proposed method.

Original languageEnglish
Pages (from-to)165-193
Number of pages29
JournalEuropean Journal of Computational Mechanics
Issue number1-2
Publication statusPublished - 2016 Mar 3
Externally publishedYes


  • Multi-objective optimisation
  • boundary element method
  • cloaking
  • electromagnetic wave
  • level set method
  • topological derivative

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mechanics of Materials
  • Mechanical Engineering


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