Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature

Lehel Banjai, Christian Lubich, Jörg Nick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Generalized impedance boundary conditions are effective approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes materials with a thin coating (with the thickness of the coating as the small scale) and strongly absorbing materials. For the acoustic scattering from generalized impedance boundary conditions, the approach taken here first determines the Dirichlet and Neumann boundary data from a system of time-dependent boundary integral equations with the usual boundary integral operators, and then the scattered wave is obtained from the Kirchhoff representation. The system of time-dependent boundary integral equations is discretized by boundary elements in space and convolution quadrature in time. The well-posedness of the problem and the stability of the numerical discretization rely on the coercivity of the Calderón operator for the Helmholtz equation with frequencies in a complex half-plane. Convergence of optimal order in the natural norms is proved for the full discretization. Numerical experiments illustrate the behaviour of the proposed numerical method.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalIMA Journal of Numerical Analysis
Volume42
Issue number1
Early online date7 Jan 2021
DOIs
Publication statusPublished - Jan 2022

Keywords

  • boundary elements
  • convolution quadrature
  • exterior domain
  • generalized impedance boundary conditions
  • wave equation

ASJC Scopus subject areas

  • General Mathematics
  • Computational Mathematics
  • Applied Mathematics

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