A robust topology optimization for enlarging working bandwidth of acoustic devices

Jincheng Qin, Hiroshi Isakari, Kouichi Taji, Toru Takahashi, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We propose a novel robust topology optimization for designing acoustic devices that are effective for broadband sound waves. Here, we define the objective function as the weighted sum of the acoustic response to an incident wave consisting of a single frequency and its standard deviation (SD) against the frequency perturbation. By approximating the SD, under the assumption that the incident frequency follows the normal distribution, with the high-order Taylor expansion of the (conventional) objective function, we deal with significant frequency variations. To calculate such an approximation, we need to calculate the high-order frequency derivatives of the state variable. Here, we define them by integral representations, which enables us to characterize them even when the state variable is defined in an unbounded domain as is often the case with wave scattering problems. We further show that, based on this definition, the high-order derivatives can efficiently be computed by a combination of the boundary element method and automatic differentiation. We also present a derivation and calculation of the topological derivative for the newly defined objective function. We install all the proposed techniques into a topology optimization method based on the level-set method to design wideband acoustic devices. The validity and effectiveness of the proposed topology optimization are confirmed through several numerical examples.

Original languageEnglish
Pages (from-to)2694-2711
Number of pages18
JournalInternational Journal for Numerical Methods in Engineering
Issue number11
Publication statusPublished - 2021 Jun 15
Externally publishedYes


  • automatic differentiation
  • boundary element method
  • level-set method
  • robust topology optimization
  • wideband acoustic device

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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