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Isogeometric topology optimization of anisotropic metamaterials for controlling high‐frequency electromagnetic wave
Author(s) -
Nishi Shinnosuke,
Yamada Takayuki,
Izui Kazuhiro,
Nishiwaki Shinji,
Terada Kenjiro
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6263
Subject(s) - topology optimization , metamaterial , homogenization (climate) , discretization , topology (electrical circuits) , finite element method , frequency domain , wave propagation , mathematical analysis , mathematics , shape optimization , floquet theory , basis function , physics , optics , thermodynamics , biodiversity , ecology , combinatorics , nonlinear system , quantum mechanics , biology
Summary 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.