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Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems

Time Domain Boundary Element Methods for the Neumann Problem: Error Estimates and Acoustic Problems
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Year:    2018

Author:    Heiko Gimperlein, Ceyhun Özdemir, Ernst P. Stephan

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1610-m2016-0494

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 1 : pp. 70–89

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

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

Author Details

Heiko Gimperlein

Ceyhun Özdemir

Ernst P. Stephan

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    Gimperlein, Heiko | Özdemir, Ceyhun | Stephan, Ernst P.

    Applied Numerical Mathematics, Vol. 152 (2020), Iss. P.49

    https://doi.org/10.1016/j.apnum.2020.01.023 [Citations: 7]

  2. Algorithmic aspects of enriched time domain boundary element methods

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    https://doi.org/10.1016/j.enganabound.2018.02.010 [Citations: 5]

  3. An enhancement of the fast time-domain boundary element method for the three-dimensional wave equation

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    https://doi.org/10.1016/j.cpc.2021.108229 [Citations: 9]

  4. Boundary elements with mesh refinements for the wave equation

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  5. Time domain boundary elements for dynamic contact problems

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    https://doi.org/10.1016/j.cma.2018.01.025 [Citations: 15]

  6. Space‐time stochastic Galerkin boundary elements for acoustic scattering problems

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    https://doi.org/10.1002/nme.7497 [Citations: 0]

  7. A residual a posteriori error estimate for the time–domain boundary element method

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  8. Time domain boundary elements for elastodynamic contact

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    Computer Methods in Applied Mechanics and Engineering, Vol. 415 (2023), Iss. P.116296

    https://doi.org/10.1016/j.cma.2023.116296 [Citations: 4]

  9. A New Approach to Space-Time Boundary Integral Equations for the Wave Equation

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    https://doi.org/10.1137/21M1420034 [Citations: 6]

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  12. On the BEM for acoustic wave problems

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    https://doi.org/10.1016/j.enganabound.2019.07.002 [Citations: 56]

  13. Transient elastodynamic analysis with a combination of convolution quadrature method and pseudo-initial condition method

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  14. hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

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    https://doi.org/10.1016/j.cma.2019.07.018 [Citations: 8]