Numerical difficulties with boundary element solutions of interior acoustic problems

Although boundary element methods have been applied to interior problems for many years, the numerical difficulties that can occur have not been thoroughly explored. Various authors have reported low-frequency breakdowns and artificial damping due to discretization errors. In this paper, it is shown through a simple example problem that the numerical difficulties depend on the solution formulation. When the boundary conditions are imposed directly, the solution suffers from artificial damping, which may potentially lead to erroneous predictions when boundary element methods are used to evaluate the performance of damping materials. This difficulty can be alleviated by first computing an impedance or admittance matrix, and then using its reactive component to derive the solution for the acoustic field. Numerical computations are used to demonstrate that this technique eliminates artificial damping, but does not correct errors in the reactive components of the impedance or admittance matrices, which then causes nonexistence and nonuniqueness difficulties at the interior resonance frequencies for hard-wall and pressure release boundary conditions, respectively. It is shown that the admittance formulation is better suited to boundary element computations for interior problems because the resonance frequencies for pressure release boundary conditions do not begin until the smallest dimension of the boundary surface is at least one half the acoustic wavelength. Aside from producing much more accurate predictions, the admittance matrix is also much easier to interpolate at low frequencies due to the absence of interior resonances. For the example problem considered, only the formulation using the reactive component of the admittance matrix produces accurate solutions as long as the surface element discretization satisfies the standard six-element-per-wavelength rule.

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Work Title Numerical difficulties with boundary element solutions of interior acoustic problems
Open Access
  1. J. B. Fahnline
  1. Boundary elements
  2. Interior acoustic problems
  3. Nonuniqueness
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
  1. Journal of Sound and Vibration
Publication Date August 20, 2008
Publisher Identifier (DOI)
Deposited March 17, 2024




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Work History

Version 1

  • Created
  • Added BE_for_Interior_ACS_JSV_Submission_b_w.pdf
  • Added Creator J. B. Fahnline
  • Published
  • Updated Keyword, Publication Date Show Changes
    • Boundary elements, Interior acoustic problems, Nonuniqueness
    Publication Date
    • 2009-01-23
    • 2008-08-20
  • Updated