An efficient quadrature for 2.5D boundary element calculations

Abstract

In recent years, the boundary element method has become a widely used tool for calculating the mitigation effects of noise barriers. However, since for large structures calculations in 3D become very inefficient, most of the standard implementations are only in 2D. This means that the noise source is implicitly assumed to be given by a coherent line source, which is not realistic in most cases. By using a Fourier transform with respect to a spatial coordinate along the length of the structure it is possible to reduce the 3D problem to several 2D problems with distinct wavenumbers which allows the simulation of more realistic noise sources and which is typically referred to as 2.5D BEM. To that end, it is necessary to numerically calculate a Fourier-like integral over all the 2D solutions. In this work, an efficient way to calculate this integral is given building on existing approaches using Clenshaw–Curtis–Filon quadrature and demodulation combined with an adaptive order-selection scheme. As BEM calculations are costly, the main focus of the method introduced lies on avoiding too many of these calculations. The efficiency of the method is illustrated using two different examples: a reflecting cylinder and an L-shaped noise barrier.