An assessment of the high frequency boundary element and visible element Rayleigh integral approximations

This paper revisits the popular Rayleigh integral approximation, and also considers the high frequency boundary element method which is similar to the Rayleigh integral. Both methods are approximations to the boundary integral equation, and can solve problems in a fraction of the time required by the conventional boundary element method. The development of both methods from the Helmholtz integral equation is demonstrated and the differences between the two methods are delineated. Both methods were compared on practical examples including a running engine, and gearbox. Theoretical examples such as a pulsating and oscillating sphere were also considered. It was concluded that both methods can reliably predict the sound power for many problems but are inaccurate for sound pressure computations.