TY - JOUR

T1 - On the spurious resonance modes of time domain integral equations for analyzing acoustic scattering from penetrable objects

AU - Chen, Rui

AU - Shi, Yifei

AU - Sayed, Sadeed Bin

AU - Lu, Mingyu

AU - Bagci, Hakan

N1 - KAUST Repository Item: Exported on 2022-04-27
Acknowledged KAUST grant number(s): 2019-CRG8-4056
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.

PY - 2022/2/16

Y1 - 2022/2/16

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/670629

UR - https://asa.scitation.org/doi/10.1121/10.0009401

UR - http://www.scopus.com/inward/record.url?scp=85125597430&partnerID=8YFLogxK

U2 - 10.1121/10.0009401

DO - 10.1121/10.0009401

M3 - Article

C2 - 35232103

SN - 0001-4966

VL - 151

SP - 1064

EP - 1076

JO - The Journal of the Acoustical Society of America

JF - The Journal of the Acoustical Society of America

IS - 2

ER -