Boundary integral formulations for acoustic modelling of high-contrast media

•The boundary integral formulation uses a mix of direct and indirect representation formulas for acoustic transmission.•A spectral analysis expresses the dependency of the formulations' eigenvalue accumulation points on the material density.•The high-contrast formulations are well-conditioned a...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2022-01, Vol.105, p.136-149
Main Authors: van 't Wout, Elwin, Haqshenas, Seyyed R., Gélat, Pierre, Betcke, Timo, Saffari, Nader
Format: Article
Language:English
Subjects:
Acoustic propagation
Acoustic scattering
Acoustics
Algorithms
Boundary element method
Boundary integral formulation
Computational acoustics
Conditioning
Contrast agents
Contrast media
Density ratio
Eigenvalues
High-contrast material
Physical properties
Scattering
Spectrum analysis
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Summary:•The boundary integral formulation uses a mix of direct and indirect representation formulas for acoustic transmission.•A spectral analysis expresses the dependency of the formulations' eigenvalue accumulation points on the material density.•The high-contrast formulations are well-conditioned at high-contrast media.•Large-scale simulations at structures with high contrasts in density and wavespeed confirm the computational efficiency. The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density, wavespeed and frequency. In particular, high contrast in density and wavespeed across a material interface leads to an ill-conditioned discretisation matrix. Therefore, the convergence of Krylov methods to solve the linear system is slow. Here, specialised boundary integral formulations are designed for the case of acoustic scattering at high-contrast media. The eigenvalues of the resulting system matrix accumulate at two points in the complex plane that depend on the density ratio and stay away from zero. The spectral analysis of the Calderón preconditioned PMCHWT formulation yields a single accumulation point. Benchmark simulations demonstrate the computational efficiency of the high-contrast Neumann formulation for scattering at high-contrast media.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.11.021