Convolution Quadrature based BEM in acoustics for absorbing boundary conditions

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In many fields of engineering the acoustic behavior has to be determined, e.g. the sound distribution in a room or the sound radiation into the surrounding. Often, the goal is to obtain a sound pressure field such that disturbing noise is reduced to an acceptable level. In room acoustics, sound absorbing materials are often used to obtain this goal. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative. Here, an indirect formulation, which uses the single layer potential, is used as basic boundary integral equation. The convolution quadrature method is applied for time discretisation, which allows a simple formulation of the Robin boundary condition in the Laplace domain. Convergence studies with a refinement in space and time show the expected rates. A realistic example for indoor acoustics, the computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics. The absorbing boundary condition shows the expected behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Original languageEnglish
Pages (from-to)23-26
Number of pages4
JournalProceedings in Applied Mathematics and Mechanics
Volume16
Issue number1
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

    Cite this

    Convolution Quadrature based BEM in acoustics for absorbing boundary conditions. / Pölz, Dominik; Sauter, Stefan; Schanz, Martin.

    In: Proceedings in Applied Mathematics and Mechanics , Vol. 16, No. 1, 01.10.2016, p. 23-26.

    Research output: Contribution to journalArticleResearchpeer-review

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    title = "Convolution Quadrature based BEM in acoustics for absorbing boundary conditions",
    abstract = "In many fields of engineering the acoustic behavior has to be determined, e.g. the sound distribution in a room or the sound radiation into the surrounding. Often, the goal is to obtain a sound pressure field such that disturbing noise is reduced to an acceptable level. In room acoustics, sound absorbing materials are often used to obtain this goal. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative. Here, an indirect formulation, which uses the single layer potential, is used as basic boundary integral equation. The convolution quadrature method is applied for time discretisation, which allows a simple formulation of the Robin boundary condition in the Laplace domain. Convergence studies with a refinement in space and time show the expected rates. A realistic example for indoor acoustics, the computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics. The absorbing boundary condition shows the expected behavior. ({\circledC} 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)",
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    author = "Dominik P{\"o}lz and Stefan Sauter and Martin Schanz",
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    AU - Pölz, Dominik

    AU - Sauter, Stefan

    AU - Schanz, Martin

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    N2 - In many fields of engineering the acoustic behavior has to be determined, e.g. the sound distribution in a room or the sound radiation into the surrounding. Often, the goal is to obtain a sound pressure field such that disturbing noise is reduced to an acceptable level. In room acoustics, sound absorbing materials are often used to obtain this goal. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative. Here, an indirect formulation, which uses the single layer potential, is used as basic boundary integral equation. The convolution quadrature method is applied for time discretisation, which allows a simple formulation of the Robin boundary condition in the Laplace domain. Convergence studies with a refinement in space and time show the expected rates. A realistic example for indoor acoustics, the computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics. The absorbing boundary condition shows the expected behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

    AB - In many fields of engineering the acoustic behavior has to be determined, e.g. the sound distribution in a room or the sound radiation into the surrounding. Often, the goal is to obtain a sound pressure field such that disturbing noise is reduced to an acceptable level. In room acoustics, sound absorbing materials are often used to obtain this goal. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative. Here, an indirect formulation, which uses the single layer potential, is used as basic boundary integral equation. The convolution quadrature method is applied for time discretisation, which allows a simple formulation of the Robin boundary condition in the Laplace domain. Convergence studies with a refinement in space and time show the expected rates. A realistic example for indoor acoustics, the computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics. The absorbing boundary condition shows the expected behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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