On the spurious resonance modes of time domain integral equations for analyzing acoustic scattering from penetrable objects

Abstract
The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the time domain potential integral equation (TDPIE), suffers from the interior resonance problem, i.e., its solution is replete with spurious modes that are excited at the resonance frequencies of the acoustic cavity in the shape of the scatterer. Numerical experiments demonstrate that, unlike the frequency-domain integral equations, the amplitude of these modes in the time domain could be suppressed to a level that does not significantly affect the solution. This is achieved by increasing the numerical solution accuracy through the use of a higher-order discretization in space and the band limited approximate prolate spheroidal wave function with high interpolation accuracy as basis function in time. The second equation is obtained by linearly combining TDPIE with its normal derivative. The solution of this equation, which is termed the time domain combined potential integral equation (TDCPIE), does not involve any spurious interior resonance modes but it is not as accurate as the TDPIE solution at non-resonance frequencies. In addition, TDCPIE's discretization calls for treatment of hypersingular integrals.

Citation
Chen, R., Shi, Y., Sayed, S. B., Lu, M., & Bagci, H. (2022). On the spurious resonance modes of time domain integral equations for analyzing acoustic scattering from penetrable objects. The Journal of the Acoustical Society of America, 151(2), 1064–1076. https://doi.org/10.1121/10.0009401

Acknowledgements
Supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. 2019-CRG8-4056. The authors would like to thank the King Abdullah University of Science and Technology Supercomputing Laboratory (KSL) for providing the required computational resources.

Publisher
Acoustical Society of America (ASA)

Journal
The Journal of the Acoustical Society of America

DOI
10.1121/10.0009401

arXiv
2108.04889

Additional Links
https://asa.scitation.org/doi/10.1121/10.0009401

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