A level set-based topology optimization method targeting metallic waveguide design problems

In this paper, we propose a level set‐based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high‐frequency range where this effect critically affects performance. One o...

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Veröffentlicht in:International journal for numerical methods in engineering 2011-09, Vol.87 (9), p.844-868
Hauptverfasser: Yamasaki, Shintaro, Nomura, Tsuyoshi, Kawamoto, Atsushi, Sato, Kazuo, Nishiwaki, Shinji
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container_issue 9
container_start_page 844
container_title International journal for numerical methods in engineering
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creator Yamasaki, Shintaro
Nomura, Tsuyoshi
Kawamoto, Atsushi
Sato, Kazuo
Nishiwaki, Shinji
description In this paper, we propose a level set‐based topology optimization method targeting metallic waveguide design problems, where the skin effect must be taken into account since the metallic waveguides are generally used in the high‐frequency range where this effect critically affects performance. One of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal. To implement this approach, we develop a boundary‐tracking scheme for the arbitrary Lagrangian Eulerian (ALE) mesh pertaining to the zero iso‐contour of the level set function that is given in an Eulerian mesh, and impose Dirichlet boundary conditions at the nodes on the zero iso‐contour in the ALE mesh to compute the electric field. Since the ALE mesh accurately tracks the zero iso‐contour at every optimization iteration, the electric field is always appropriately computed during optimization. For the sensitivity analysis, we compute the nodal coordinate sensitivities in the ALE mesh and smooth them by solving a Helmholtz‐type partial differential equation. The obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the Eulerian mesh, and the level set function is updated based on the computed normal velocity. Finally, the utility of the proposed method is discussed through several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.
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subjects Applied sciences
arbitrary Lagrangian Eulerian method
Circuit properties
Design engineering
Dirichlet problem
Electric fields
Electric, optical and optoelectronic circuits
Electronics
Exact sciences and technology
level set method
Mathematical analysis
Mathematical models
metallic waveguide
Microwave circuits, microwave integrated circuits, microwave transmission lines, submillimeter wave circuits
Optimization
Skin effect
smoothed sensitivity
topology optimization
Waveguides
title A level set-based topology optimization method targeting metallic waveguide design problems
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