An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

Abstract

Effective use of the Fourier series boundary element method ͑FBEM͒ for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general.

A high-order Nyström discretization scheme for boundary integral equations defined on rotationally symmetric surfaces

“…Advantages of a BIE approach include a reduction in dimensionality, often a radical improvement in the conditioning of the mathematical equation to be solved, a natural way of handling problems defined on exterior domains, and a relative ease in implementing high-order discretization schemes, see, e.g., [3]. The observation that BIEs on rotationally symmetric surfaces can conveniently be solved by recasting them as a sequence of BIEs on a generating curve has previously been exploited in the context of stress analysis [4], scattering [9,17,22,23,24], and potential theory [12,19,20,21]. Most of these approaches have relied on collocation or Galerkin discretizations and have generally used low-order accurate discretizations.…”

Sound Radiation From a Vibrating Railway Wheel

“…This allows an axisymmetric structure to be modelled with non-axisymmetric boundary conditions, using a Fourier series expansion [14]. Since the vibration of a wheel is dominated by its modes, the sound radiation has been calculated for each individual wheel mode in the range of interest.…”

An efficient and highly accurate solver for multi-body acoustic scattering problems involving rotationally symmetric scatterers

“…Despite the fact that the kernel in the BIE is singular, high accuracy can be maintained using the correction techniques of [16,13]. Following [20], we exploit the rotational symmetry of each body to decouple the local equations as a sequence of equations defined on a generating contour [22,23,17,25,24]. This dimension reduction technique requires an efficient method for evaluating the fundamental solution of the Helmholtz equation in cylindrical coordinates (the so called "toroidal harmonics"); we use the technique described in [26].…”