Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems

Heiko Gimperlein; Ceyhun Oezdemir; Ernst P. Stephan

doi:10.4208/jcm.1610-m2016-0494

Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems

Heiko Gimperlein, Ceyhun Oezdemir, Ernst P. Stephan

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

96 Downloads (Pure)

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 convergenc of our boundary element scheme and compare it with the numerical approximations obtainefrom an integral equation of the second kind. Computations in a half-space illustratthe influence of the reflection properties of a flat street.

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	1 Feb 2018
DOIs	https://doi.org/10.4208/jcm.1610-m2016-0494
Publication status	Published - Feb 2018

Access to Document

10.4208/jcm.1610-m2016-0494

Download pdf
The Work may be reproduced by any means for educational and scientific purposes by the Author(s) or by others without fee or permission with the exception of reproduction by services that collect fees for delivery of documents.
Accepted author manuscript, 915 KBLicence: All Rights Reserved

http://www.global-sci.org/jcm/galley/JCM2016-0494.pdfLicence: All Rights Reserved

Cite this

@article{230125415e214b9aa977b8b0d7d094fc,

title = "Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems",

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 convergenc of our boundary element scheme and compare it with the numerical approximations obtainefrom an integral equation of the second kind. Computations in a half-space illustratthe influence of the reflection properties of a flat street.",

author = "Heiko Gimperlein and Ceyhun Oezdemir and Stephan, {Ernst P.}",

year = "2018",

month = feb,

doi = "10.4208/jcm.1610-m2016-0494",

language = "English",

volume = "36",

pages = "70--89",

journal = "Journal of Computational Mathematics",

issn = "0254-9409",

publisher = "Inst. of Computational Mathematics and Sc./Eng. Computing",

number = "1",

}

TY - JOUR

T1 - Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems

AU - Gimperlein, Heiko

AU - Oezdemir, Ceyhun

AU - Stephan, Ernst P.

PY - 2018/2

Y1 - 2018/2

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 convergenc of our boundary element scheme and compare it with the numerical approximations obtainefrom an integral equation of the second kind. Computations in a half-space illustratthe 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 convergenc of our boundary element scheme and compare it with the numerical approximations obtainefrom an integral equation of the second kind. Computations in a half-space illustratthe influence of the reflection properties of a flat street.

U2 - 10.4208/jcm.1610-m2016-0494

DO - 10.4208/jcm.1610-m2016-0494

M3 - Article

SN - 0254-9409

VL - 36

SP - 70

EP - 89

JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

IS - 1

ER -

Time domain boundary element methods for the Neumann problem: Error estimates and acoustic problems

Abstract

Access to Document

Fingerprint

Cite this