 Convolution quadrature based BEM in acoustics for absorbing boundary conditions

Pölz, Dominik; Sauter, Stefan A; Schanz, Martin (2016). Convolution quadrature based BEM in acoustics for absorbing boundary conditions. Proceedings in Applied Mathematics and Mechanics, 16(1):23-26.

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.

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.

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