Conventional boundary element techniques: Recent developments and opportunities

Over the last three to four decades, the boundary element method (BEM) has become a standard tool for low and mid-frequency computations. A large fraction of publications on BEM in acoustics over the recent 15 years has been focused on efficiency and how to make it possible to apply the methods to large-scale models at higher frequencies. While these so-called fast boundary element techniques have been implemented into commercial and open source codes, it has turned out that even rather basic aspects of the method are not sufficiently clarified so far. With respect to these aspects and some opportunities of BEM, this paper is divided into four parts. At first, discretization rules will be critically discussed. It is common to assume that a fixed number of elements per wavelength is sufficient to predict the numeric error. However, it will be shown that, similar to the finite element method, the rule of a fixed number of elements per wavelength is insufficient for large wave numbers. This behaviour can be understood as a pollution effect and should be considered when meshing objects. The second part of the talk will discuss the non-uniqueness problem. A very reliable method to overcome this problem has been proposed by and named after Burton and Miller. While this method is using only one parameter, it turned out that approximately 50% of the literature on the Burton and Miller method is using a wrong sign for it. It will be discussed why this has happened and what the consequences are. The remaining two parts of the presentation are related to applications of BEM. At first, a method is described which can be easily and efficiently applied to noise barriers. Most papers in literature are based on a 2d or a 2.5d formulation. However, modelling a realistic barrier with varying structures such as Helmholtz resonators along the length of the barrier requires a 3d model. The author presents a very simple 3d boundary element formulation which assumes that barrier, sources and sound pressure solution are periodic along the barrier. Since the periodicity is truncated in the far-field, this method has been called a quasi-periodic BEM. The final part of the paper considers a panel contribution analysis. Panel contribution analysis is useful to identify hot spots at the surface of an enclosed domain or a radiator. It makes use of the fact that the system matrices of a numerical model contain much more information than what is required to evaluate the sound pressure based on some sources. The paper discuss two different concepts including one which returns a non-negative intensity allowing to eliminate acoustic short circuits. Finally, the paper will be summarized and other work of the author on BEM is briefly discussed.