A frequency domain finite element solver for acoustic simulations of 3D rooms with microperforated panel absorbers

Microperforated panel (MPP) absorbers, which provide broadband sound absorption without the use of fibrous materials, have favorable material properties that support recyclability, flexibility of design, hygiene demands, and cleaning. Many earlier studies have specifically examined the development of absorbers themselves. However, to use the absorption performance of MPP absorbers sufficiently in room acoustic applications, it is beneficial to develop accurate prediction methods of sound fields in rooms with MPP absorbers. Such methods are expected to be useful for room acoustics design and absorber design tools. This study constructs a frequency domain finite element (FE) solver for acoustic simulations of a practical sized room with MPP absorbers. Then the accuracy and effectiveness are evaluated. In the FE solver, spatial domains are discretized by fourth-order accurate FEs in terms of dispersion error, and MPP absorbers are modeled using first-order hexahedral limp MPP elements that can deal with sound propagation in the backing structure of absorbers. First, the accuracy of present FE solver is demonstrated using impedance tube problems in comparison with conventional second-order accurate FEs. Results show higher convergence of solutions for the present FE solver. Then, exploration of an iterative solver for efficient multi-frequency analyses reveals that the recently developed CSQMOR is a faster and more stable solver. Finally, comparison with a conventional surface impedance model based on a locally reacting assumption confirms the effectiveness of present FE solver by presenting the importance of dealing with the incident angle dependence of reactance of a rigid-backed air cavity in the modeling of single-leaf MPP absorbers.