Isogeometric topology optimization of anisotropic metamaterials for controlling high-frequency electromagnetic wave

Shinnosuke Nishi, Takayuki Yamada, Kazuhiro Izui, Shinji Nishiwaki, Kenjiro Terada

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


This study presents a level set–based topology optimization with isogeometric analysis (IGA) for controlling high-frequency electromagnetic wave propagation in a domain with periodic microstructures (unit cells). The high-frequency homogenization method is applied to characterize the macroscopic high-frequency waves in periodic heterogeneous media whose wavelength is comparative to or smaller than the representative length of a unit cell. B-spline basis functions are employed for the IGA discretization procedure to improve the performance of electromagnetic wave analysis in a unit cell and topology optimization. Also, to keep the same order of continuity on the periodic boundaries as on other element edges in the domain, we propose the extended domain approach, while incorporating Floquet periodic boundary condition (FPBC). Two types of optimization problems are taken as examples to demonstrate the effectiveness of the proposed method in comparison with the standard finite element analysis (FEA). The optimization results provide optimized topologies of unit cells qualified as anisotropic metamaterials with hyperbolic and bidirectional dispersion properties at the macroscale.

Original languageEnglish
Pages (from-to)1218-1247
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
Publication statusPublished - 2020 Mar 30


  • anisotropic metamaterial
  • high-frequency homogenization
  • isogeometric analysis
  • level-set method
  • topology optimization


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