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

18 Citations (Scopus)

135 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

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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.\}",

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AU - Oezdemir, Ceyhun

AU - Stephan, Ernst P.

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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

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JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

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

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