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Detecting Near Resonances in Acoustic Scattering

by L. Grubisic and R. Hiptmair and D. Renner

(Report number 2022-38)

Abstract
We propose and study a method for finding quasi-resonances for a linear acoustic transmission problem in frequency domain. Starting from an equivalent boundary-integral equation we perform Galerkin boundary element discretization and look for the minima of the smallest singular value of the resulting matrix as a function of the wave number \(k\). We develop error estimates for the impact of Galerkin discretization on singular values and devise a heuristic adaptive algorithm for finding the minima in prescribed \(k\)-intervals. Our method exclusively relies on the solution of eigenvalue problems for real \(k\), in contrast to alternative approaches that rely on extension to the complex plane.

Keywords: Acoustic scattering, quasi-resonances, boundary integral equations, boundary element method, singular values, Wielandt matrix, zero finding,

@Techreport{GHR22_1026,
  author = {L. Grubisic and R. Hiptmair and D. Renner},
  title = {Detecting Near Resonances in Acoustic Scattering},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-38},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-38.pdf },
  year = {2022}
}

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