A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term

Shixu Meng, Othman Oudghiri-Idrissi, Bojan B. Guzina

Research output: Contribution to journalArticlepeer-review

Abstract

We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in an unbounded medium (Formula presented.) ((Formula presented.)), we first use the (Floquet-)Bloch transform to formulate an equivalent variational problem in a bounded domain. By investigating the source term's projection onto certain periodic functions, the second-order model can then be derived via asymptotic expansion of the Bloch eigenfunction and the germane dispersion relationship. We establish the convergence of the second-order homogenized solution, and we include numerical examples to illustrate the convergence result.

Original languageEnglish (US)
JournalApplicable Analysis
DOIs
StateAccepted/In press - 2021

Bibliographical note

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • (Floquet-)Bloch transform
  • band gap
  • dynamic homogenization
  • finite frequency
  • variational formulation
  • Waves in periodic media

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