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Volume 36, Issue 1
Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

Heiko Gimperlein, Ceyhun Özdemir & Ernst P. Stephan

DOI: 10.4208/jcm.1610-m2016-0494

J. Comp. Math., 36 (2018), pp. 70-89.

Published online: 2018-02

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  • Abstract

We investigate time domain boundary element methods for the wave equation in $\mathbb{R}^3$, 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

Time domain boundary element method, Wave equation, Neumann problem, Error estimates, Sound radiation.

  • AMS Subject Headings

65N38, 65R20, 74J05.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

h.gimperlein@hw.ac.uk (Heiko Gimperlein)

oezdemir@ifam.uni-hannover.de (Ceyhun Özdemir)

stephan@ifam.uni-hannover.de (Ernst P. Stephan)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-70, author = {Gimperlein , HeikoÖzdemir , Ceyhun and Stephan , Ernst P.}, title = {Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {1}, pages = {70--89}, abstract = {

We investigate time domain boundary element methods for the wave equation in $\mathbb{R}^3$, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1610-m2016-0494}, url = {http://global-sci.org/intro/article_detail/jcm/10583.html} }
TY - JOUR T1 - Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems AU - Gimperlein , Heiko AU - Özdemir , Ceyhun AU - Stephan , Ernst P. JO - Journal of Computational Mathematics VL - 1 SP - 70 EP - 89 PY - 2018 DA - 2018/02 SN - 36 DO - http://doi.org/10.4208/jcm.1610-m2016-0494 UR - https://global-sci.org/intro/article_detail/jcm/10583.html KW - Time domain boundary element method, Wave equation, Neumann problem, Error estimates, Sound radiation. AB -

We investigate time domain boundary element methods for the wave equation in $\mathbb{R}^3$, 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.

Gimperlein , HeikoÖzdemir , Ceyhun and Stephan , Ernst P.. (2018). Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems. Journal of Computational Mathematics. 36 (1). 70-89. doi:10.4208/jcm.1610-m2016-0494
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