Text European Acoustics Association

Linear acoustics

Wave propagation as a solution of the wave equation, including scattering and radiation problems, interior and exterior problems, time domain and frequency domain problems.

Related EAA editorial fields: General Linear Acoustics. Computational and Numerical Acoustics, Room Acoustics, Physical Acoustics, Ultrasonics.

Currently the following benchmark cases are available:


This benchmark problem may be considered as waves traveling through a duct. Although a smooth solution is expected over the entire frequency range, the numerical solution may be unstable if modes perpendicular to the traveling waves occur.

This benchmark can be used to study the eigenvalue problem with arbitrary admittance boundary conditions, discusses the accuracy of mode superposition for reconstruction of the solution in frequency domain, as well as study the convergence of your formulation towards h- and p-refinement.

A detailed description with references can be found in LA_Case1_Duct.pdf, opens a file in a new window.


This benchmark problem consists of  a vibrating surface, which coincides with the spherical one. The plain surfaces of the missing octant are assigned a zero admittance. Thereby, the radiator allows construction of a smooth solution that will make it easy to identify solution failures caused by the ill–conditioning of the integral operator for techniques that solve the Helmholtz equation in an integral formulation, i.e. the irregular frequencies. Furthermore, the cat’s eye structure is a more complicated shape than a sphere and hence, the solution is expected to expose more irregular frequencies in a BEM solution than the sphere.

A detailed description with references can be found in LA_Case2_CatEye.pdf, opens a file in a new window.

Available solutions:

Steffen MarburgBoundary Element Method LA_Case2_CatEye_SteffenMarburg.pdf, opens a file in a new window


A radiatterer is a geometry that both acts as a radiator of sound as well as it scatterers the radiated sound waves. In addition to the problem of irregular frequencies, it is well suited to compare resonance amplitudes yielded by different methods and different types of finite and boundary elements. Furthermore, the numerical methods should investigate whether mesh refinement in regions with large gradients is necessary or can be neglected.

A detailed description with references can be found in LA_Case3_Radiatterer.pdf, opens a file in a new window.

Available solutions:

Steffen Marburg, Boundary Element Method, LA_Case3_Radiatterer_SteffenMarburg.pdf, opens a file in a new window


The PAC-MAN geometry is the two-dimensional equivalent to the three-dimensional cat’s eye geometry. As shown in Fig. 1, it is a circle of radius  with an angular cut-out ranging from (measured from the x-axis) and . An analytical solution of the sound field inside the cut-out and outside the PAC-MAN has been derived in Ziegelwanger-Reiter-JCP, opens an external URL in a new window . The PAC-MAN problem is suited for radiation and scattering.

The description with references can be found in PACMAN_benchmark_case.pdf, opens a file in a new window.

H. Ziegelwanger and P. Reiter, Analytic formulation of radiated and scattered sound, PACMAN.zip, opens a file in a new window

The Benchmark for Room Acoustical Simulation (BRAS) contains seven acoustical reference scenes that are intended for the evaluation of room acoustical simulation software. The reference scenes isolate acoustic phenomena such as reflection, scattering, and diffraction.

For the scientific publication by Aspöck, Lukas; Brinkmann, Fabian; Ackermann, David; Weinzierl, Stefan; Vorländer, Michael we refer to https://doi.org/10.1016/j.apacoust.2020.107867, opens an external URL in a new window and all details can be found at https://dx.doi.org/10.14279/depositonce-6726.3, opens an external URL in a new window.