Development of 3D PUFEM with linear tetrahedral elements for the simulation of acoustic waves in enclosed cavities

Abstract

This work is concerned with the numerical simulation of sound pressure field in three-dimensional cavities in which absorbing materials are present. Standard techniques such as the Finite Element Method are known to be extremely demanding computationally when the frequency increases and thus limited to low frequency applications. To alleviate these difficulties, an alternative formulation based on the Partition of Unity Finite Element Method is proposed. The method involves enriching the approximation finite element space by expanding the acoustic pressure in a set of plane waves propagating in various directions over the unit sphere. Particular attention is devoted to the fast and accurate computation of highly oscillatory integrals which is required by the method. Convergence studies show that these wave finite elements allow to capture accurately the wave field with a number of degrees of freedom that only grows quadratically with the frequency yielding drastic data reduction compared to classical FEM. Results of practical interest are shown for the case of a sound source placed in a reverberation room with absorbing materials.