A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials. / Otomori, Masaki; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji; Andkjær, Jacob.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 237-240, 2012, p. 192-211.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Author

Otomori, Masaki; Yamada, Takayuki; Izui, Kazuhiro; Nishiwaki, Shinji; Andkjær, Jacob / A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 237-240, 2012, p. 192-211.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

Bibtex

@article{ec7da2e973ad4824a5b0fca34db6dac4,
title = "A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials",
keywords = "Dielectric metamaterials, Negative permeability, Topology optimization, Finite Element Method, Level set method, Adjoint Variable Method",
publisher = "Elsevier BV",
author = "Masaki Otomori and Takayuki Yamada and Kazuhiro Izui and Shinji Nishiwaki and Jacob Andkjær",
year = "2012",
doi = "10.1016/j.cma.2012.04.022",
volume = "237-240",
pages = "192--211",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",

}

RIS

TY - JOUR

T1 - A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials

A1 - Otomori,Masaki

A1 - Yamada,Takayuki

A1 - Izui,Kazuhiro

A1 - Nishiwaki,Shinji

A1 - Andkjær,Jacob

AU - Otomori,Masaki

AU - Yamada,Takayuki

AU - Izui,Kazuhiro

AU - Nishiwaki,Shinji

AU - Andkjær,Jacob

PB - Elsevier BV

PY - 2012

Y1 - 2012

N2 - This paper presents a level set-based topology optimization method for the design of negative permeability dielectric metamaterials. Metamaterials are artificial materials that display extraordinary physical properties that are unavailable with natural materials. The aim of the formulated optimization problem is to find optimized layouts of a dielectric material that achieve negative permeability. The presence of grayscale areas in the optimized configurations critically affects the performance of metamaterials, positively as well as negatively, but configurations that contain grayscale areas are highly impractical from an engineering and manufacturing point of view. Therefore, a topology optimization method that can obtain clear optimized configurations is desirable. Here, a level set-based topology optimization method incorporating a fictitious interface energy is applied to a negative permeability dielectric metamaterial design problem. The optimization algorithm uses the Finite Element Method (FEM) for solving the equilibrium and adjoint equations, and design problems are formulated for both two- and three-dimensional cases. First, the level set-based topology optimization method is explained, and the optimization problems for the design of metamaterials are then discussed. Several optimum design examples for the design of dielectric metamaterials that demonstrate negative effective permeability at prescribed frequencies are provided to confirm the utility and validity of the presented method.

AB - This paper presents a level set-based topology optimization method for the design of negative permeability dielectric metamaterials. Metamaterials are artificial materials that display extraordinary physical properties that are unavailable with natural materials. The aim of the formulated optimization problem is to find optimized layouts of a dielectric material that achieve negative permeability. The presence of grayscale areas in the optimized configurations critically affects the performance of metamaterials, positively as well as negatively, but configurations that contain grayscale areas are highly impractical from an engineering and manufacturing point of view. Therefore, a topology optimization method that can obtain clear optimized configurations is desirable. Here, a level set-based topology optimization method incorporating a fictitious interface energy is applied to a negative permeability dielectric metamaterial design problem. The optimization algorithm uses the Finite Element Method (FEM) for solving the equilibrium and adjoint equations, and design problems are formulated for both two- and three-dimensional cases. First, the level set-based topology optimization method is explained, and the optimization problems for the design of metamaterials are then discussed. Several optimum design examples for the design of dielectric metamaterials that demonstrate negative effective permeability at prescribed frequencies are provided to confirm the utility and validity of the presented method.

KW - Dielectric metamaterials

KW - Negative permeability

KW - Topology optimization

KW - Finite Element Method

KW - Level set method

KW - Adjoint Variable Method

U2 - 10.1016/j.cma.2012.04.022

DO - 10.1016/j.cma.2012.04.022

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

VL - 237-240

SP - 192

EP - 211

ER -