On the Robustness and Efficiency of the Plane-Wave-Enriched FEM with Variable q-Approach on the 2D Room Acoustics Problem

Abstract

Partition of unity finite element method with plane wave enrichment (PW-FEM) uses a shape function with a set of plane waves propagating in various directions. For room acoustic simulations in a frequency domain, PW-FEM can be an efficient wave-based prediction method, but its practical applications and especially its robustness must be studied further. This study elucidates PW-FEM robustness via 2D real-scale office room problems including rib-type acoustic diffusers. We also demonstrate PW-FEM performance using a sparse direct solver and a high-order Gauss–Legendre rule with a recently developed rule for ascertaining the number of integration points against the classical linear and quadratic FEMs. Numerical experiments investigating mesh size and room geometrical complexity effects on the robustness of PW-FEM demonstrated that PW-FEM becomes more robust at wide bands when using a mesh in which the maximum element size maintains a comparable value to the wavelength of the upper-limit frequency. Moreover, PW-FEM becomes unstable with lower spatial resolution mesh, especially for rooms with complex shape. Comparisons of accuracies and computational costs of linear and quadratic FEM revealed that PW-FEM requires twice the computational time of the quadratic FEM with a mesh having spatial resolution of six elements per wavelength, but it is highly accurate at wide bands with lower memory and with markedly fewer degrees of freedom. As an additional benefit of PW-FEM, the impulse response waveform of quadratic FEM in a time domain was found to deteriorate over time, but the PW-FEM waveform can maintain accurate waveforms over a long time.