A Review of Finite Element Methods for Room Acoustics

Accurate predictions of the wave-dominated region of an acoustic field in a room can be generated using wave-based computational methods. One such method is the finite element method (FEM). With presently available computing power and advanced numerical techniques, it is possible to obtain FEM predictions of sound fields in rooms with complicated geometries and complex boundary conditions in realistic time frames. The FEM has been continuously developed since its inception and attempts to provide solutions in real time using finite element-based methods are beginning to appear in the literature; these developments are especially interesting for auralization and virtual acoustics applications. To support these efforts, and provide a resource for neophytes, the use of the FEM for room acoustics is reviewed in this article. A history is presented alongside examples of the method's derivation, implementation, and solutions. The current challenges and state-of-the-art are also presented, and it is found that the most recent contributions to the field make use of one or a mixture of the following: the finite element-based discontinuous Galerkin method, extended reaction boundary conditions written in the frequency domain but solved in the time domain, and the solution of large-scale models using parallel processing and graphics processing units.