Concerning the cause of instability in time-stepping boundary element methods applied to the exterior acoustic problem

H. Wang, D. Henwood, Paul Harris, R. Chakrabarti

Research output: Contribution to journalArticle

Abstract

The boundary element method (BEM) in its simple form when solving the exterior acoustic problem in the frequency domain has difficulties at the frequencies of internal resonances of the closed structure. The corresponding time domain form of the exterior problem often exhibits instabilities in the time-stepping process. The link between these two features is investigated by relating the eigenvalues of the iterating matrix of the time-stepping process to damped frequencies. Numerical evidence from a problem with an analytic solution, and from a loudspeaker response are given. The suggested link implies that instability comes from numerical errors super-imposed on a more fundamental problem and may be best tackled through a time domain technique corresponding to the methods already available in the frequency domain.
Original languageEnglish
Pages (from-to)289-297
Number of pages9
JournalJournal of Sound and Vibration
Volume305
Issue number1-2
Publication statusPublished - Aug 2007

Fingerprint

boundary element method
acoustics
causes
loudspeakers
eigenvalues
matrices

Cite this

@article{949414e0a5fc4dfbb062365636659c03,
title = "Concerning the cause of instability in time-stepping boundary element methods applied to the exterior acoustic problem",
abstract = "The boundary element method (BEM) in its simple form when solving the exterior acoustic problem in the frequency domain has difficulties at the frequencies of internal resonances of the closed structure. The corresponding time domain form of the exterior problem often exhibits instabilities in the time-stepping process. The link between these two features is investigated by relating the eigenvalues of the iterating matrix of the time-stepping process to damped frequencies. Numerical evidence from a problem with an analytic solution, and from a loudspeaker response are given. The suggested link implies that instability comes from numerical errors super-imposed on a more fundamental problem and may be best tackled through a time domain technique corresponding to the methods already available in the frequency domain.",
author = "H. Wang and D. Henwood and Paul Harris and R. Chakrabarti",
year = "2007",
month = "8",
language = "English",
volume = "305",
pages = "289--297",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
number = "1-2",

}

Concerning the cause of instability in time-stepping boundary element methods applied to the exterior acoustic problem. / Wang, H.; Henwood, D.; Harris, Paul; Chakrabarti, R.

In: Journal of Sound and Vibration, Vol. 305, No. 1-2, 08.2007, p. 289-297.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Concerning the cause of instability in time-stepping boundary element methods applied to the exterior acoustic problem

AU - Wang, H.

AU - Henwood, D.

AU - Harris, Paul

AU - Chakrabarti, R.

PY - 2007/8

Y1 - 2007/8

N2 - The boundary element method (BEM) in its simple form when solving the exterior acoustic problem in the frequency domain has difficulties at the frequencies of internal resonances of the closed structure. The corresponding time domain form of the exterior problem often exhibits instabilities in the time-stepping process. The link between these two features is investigated by relating the eigenvalues of the iterating matrix of the time-stepping process to damped frequencies. Numerical evidence from a problem with an analytic solution, and from a loudspeaker response are given. The suggested link implies that instability comes from numerical errors super-imposed on a more fundamental problem and may be best tackled through a time domain technique corresponding to the methods already available in the frequency domain.

AB - The boundary element method (BEM) in its simple form when solving the exterior acoustic problem in the frequency domain has difficulties at the frequencies of internal resonances of the closed structure. The corresponding time domain form of the exterior problem often exhibits instabilities in the time-stepping process. The link between these two features is investigated by relating the eigenvalues of the iterating matrix of the time-stepping process to damped frequencies. Numerical evidence from a problem with an analytic solution, and from a loudspeaker response are given. The suggested link implies that instability comes from numerical errors super-imposed on a more fundamental problem and may be best tackled through a time domain technique corresponding to the methods already available in the frequency domain.

M3 - Article

VL - 305

SP - 289

EP - 297

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 1-2

ER -