Topology optimization of magnetic shielding using level-set function combined with element-based topological derivatives

Reona Hoshino*, Yoshifumi Okamoto, Shinji Wakao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Purpose: Shape optimization using the level-set method is one of the most effective automatic design tools for electromagnetic machines. While level-set method has the advantage of being able to suppress unfeasible shape, it has a weakness of being unable to handle complex topology changes such as perforate at material region. With this method, it is only possible to define simple connected topology, and it is difficult to determine the optimal shape which has holes. Therefore, it is important to efficiently expand the searching area in the optimization process with level-set method. Design/methodology/approach: In this paper, the authors introduce the newly defined hole sensitivity which is based on concept of topological derivatives, and combine it with level-set method to effectively create holes in the search process. Furthermore, they consider a variable bandwidth of gray scale, which indicates the transition width between air and magnetic body and combine it with the hole creation method described above. With these methods, the authors aim to expand the searching area in comparison with the conventional level-set method. Findings: As a result of applying the proposed methods to a magnetic shielding problem, the multi-layered shielding which effectively reduces the magnetic flux in the target area, is successfully produced. Originality/value: The proposed methods enable us to effectively create a hole and to expand the searching area in the topology optimization process unlike in the case of conventional level-set method.

Original languageEnglish
Pages (from-to)718-729
Number of pages12
JournalCOMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Issue number2
Publication statusPublished - 2018 Mar 5


  • Element-based topological derivatives
  • Level-set method
  • Magnetic shield
  • Magnetostatic problem

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Applied Mathematics


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