Development of the partition of unity finite element method for the 3D analysis of interior sound fields
Regular paper
Université de technologie de Compiègne
Tuesday 2 june, 2015, 14:40 - 15:00
0.7 Lisbon (47)
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 (FEM) 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 (PUFEM) 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
oscillating 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 on
the wall.