A topology optimization of open acoustic waveguides based on a scattering matrix method

Kei Matsushima, Hiroshi Isakari, Toru Takahashi, Toshiro Matsumoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai–Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.

Original languageEnglish
Article number102987
JournalWave Motion
Publication statusPublished - 2022 Aug


  • Acoustic waveguide
  • Bound state in the continuum
  • Boundary element method
  • Scattering matrix
  • Topology optimization

ASJC Scopus subject areas

  • Modelling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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