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A level set‐based topology optimization method targeting metallic waveguide design problems
Author(s) -
Yamasaki Shintaro,
Nomura Tsuyoshi,
Kawamoto Atsushi,
Sato Kazuo,
Nishiwaki Shinji
Publication year - 2011
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.3135
Subject(s) - level set (data structures) , level set method , topology optimization , mathematics , topology (electrical circuits) , boundary (topology) , eulerian path , signed distance function , helmholtz equation , shape optimization , helmholtz free energy , mathematical optimization , boundary value problem , mathematical analysis , algorithm , computer science , finite element method , physics , lagrangian , artificial intelligence , segmentation , combinatorics , quantum mechanics , image segmentation , thermodynamics
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.