Topological shape optimization of electromagnetic problems using level set method and radial basis function

Hokyung Shim, Vinh Thuy Tran Ho, Semyung Wang, Daniel A. Tortorelli

Research output: Contribution to journalArticlepeer-review


This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free boundaries (dynamic interfaces) represented in the level set model determine the optimal shape via the topological changes. In order to improve efficiency of the level set evolution, a radial basis function (RBF) is introduced. The RBF allows the algorithm to create new holes inside the material domain, which lead to an approximately global optimum point. The optimization technique is illustrated using 2D examples captured from 3D level set configuration and the resulting optimum shape is compared with the conventional topology optimization. This work highlights that the derived shape sensitivity is verified using the finite difference method (FDM) through an example, and the level set method is validated as a promising optimization tool in a practical electromagnetic problem. Also, the level set based optimization shows a clear void-solid pattern without gray areas that the topology optimization yields.

Original languageEnglish (US)
Pages (from-to)175-202
Number of pages28
JournalCMES - Computer Modeling in Engineering and Sciences
Issue number2
StatePublished - 2008


  • Gradientbased optimization
  • Level set method
  • Radial basis function
  • Shape derivative
  • Shape optimization

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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