Details
| Original language | English |
|---|---|
| Pages (from-to) | 70-89 |
| Number of pages | 20 |
| Journal | Journal of Computational Mathematics |
| Volume | 36 |
| Issue number | 1 |
| Early online date | 11 Oct 2017 |
| Publication status | Published - 2018 |
Abstract
We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.
Keywords
- Error estimates, Neumann problem, Sound radiation, Time domain boundary element method, Wave equation
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
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In: Journal of Computational Mathematics, Vol. 36, No. 1, 2018, p. 70-89.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Time domain boundary element methods for the Neumann problem
T2 - Error estimates and acoustic problems
AU - Gimperlein, Heiko
AU - Özdemir, Ceyhun
AU - Stephan, Ernst P.
N1 - Funding Information: Acknowledgments. Parts of this work were funded by BMWi under the project SPERoN 2020, part II, Leiser Straßenverkehr, grant number 19 U 10016 F. H. G. acknowledges support by ERC Advanced Grant HARG 268105. C. O. is supported by a scholarship of the Avicenna foundation.
PY - 2018
Y1 - 2018
N2 - We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.
AB - We investigate time domain boundary element methods for the wave equation in R3, with a view towards sound emission problems in computational acoustics. The Neumann problem is reduced to a time dependent integral equation for the hypersingular operator, and we present a priori and a posteriori error estimates for conforming Galerkin approximations in the more general case of a screen. Numerical experiments validate the convergence of our boundary element scheme and compare it with the numerical approximations obtained from an integral equation of the second kind. Computations in a half-space illustrate the influence of the reflection properties of a flat street.
KW - Error estimates
KW - Neumann problem
KW - Sound radiation
KW - Time domain boundary element method
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=85041479428&partnerID=8YFLogxK
U2 - 10.4208/JCM.1610-M2016-0494
DO - 10.4208/JCM.1610-M2016-0494
M3 - Article
AN - SCOPUS:85041479428
VL - 36
SP - 70
EP - 89
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
SN - 0254-9409
IS - 1
ER -