Numerical Damping in the Acoustic Boundary Element Method

The frequency domain acoustic boundary element method has been comprehensively studied and is widely used in the community of acoustical engineering. Therefore, it has been surprising for the author that, apparently, the phenomenon of numerical damping in the conventional boundary element formulation seems to be unknown. At least, the author was not able to find any discussion about it in literature. Numerical damping is well-known, often even artificially and on purpose introduced for the time domain solution. However, it is contained in the conventional boundary element formulation and it easily reaches a size which must not be neglected. The simple numerical example of a duct demonstrates this phenomenon. It is shown that a real fundamental solution can avoid numerical damping but it may introduce instability problems as known from the literature. This contribution is motivated by the idea of igniting a scientific discussion about the source and the importance of numerical damping for the acoustic boundary element method.