Abstract
Predicting room acoustics using wave-based numerical methods has attracted great attention in recent years. Nevertheless, wave-based predictions are generally computationally expensive for room acoustics simulations because of the large dimensions of architectural spaces, the wide audible frequency ranges, the complex boundary conditions, and inherent error properties of numerical methods. Therefore, development of an efficient wave-based room acoustic solver with smaller computational resources is extremely important for practical applications. This paper describes a preliminary study aimed at that development. We discuss the potential of the Partition of Unity Finite Element Method (PUFEM) as a room acoustic solver through the examination with 2D real-scale room acoustic problems. Low-order finite elements enriched by plane waves propagating in various directions are used herein. We examine the PUFEM performance against a standard FEM via two-room acoustic problems in a single room and a coupled room, respectively, including frequency-dependent complex impedance boundaries of Helmholtz resonator type sound absorbers and porous sound absorbers. Results demonstrated that the PUFEM can predict wideband frequency responses accurately under a single coarse mesh with much fewer degrees of freedom than the standard FEM. The reduction reaches O ( 10 − 2 ) at least, suggesting great potential of PUFEM for use as an efficient room acoustic solver.
Highlights
The degrees of freedom (DOF) in Partition of Unity Finite Element Method (PUFEM) is defined as the product of plane wave numbers q for enrichment and nodes Nnode i.e., DOF = q × Nnode
The results demonstrate clearly that the PUFEM can perform well for more complex coupled fields with a small amount of DOF
We discussed the potential of plane-wave-enriched finite element method (FEM) as a room acoustic solver to solve the issues on wave-based room acoustic simulations via performance examination on 2D real-scale room acoustic problems with realistic boundary conditions in comparison with the standard second-order accurate FEM
Summary
Acoustic simulation methods are necessary tools for predicting impulse responses or frequency responses of room spaces in architectural acoustics design. The huge computational effort necessary for performing reliable acoustic simulations in real-sized rooms using FEM stems from the large dimension of spaces, the broad frequency range of interest, the complicated boundary conditions, and an inherent error property of FEM. To maintain the error within an acceptable level, the discretization of spaces, i.e., mesh generation, must be performed with consideration of a rule of thumb, e.g., for linear elements spatial discretization of 10 elements per wavelength at least This discretization rule imposes the use of a large FE models with many DOF for acoustic simulation of a real-sized room, making the solution of the problem prohibitively expensive. The development of room acoustic FEM solvers able to perform reliable simulations with an FE model having much fewer DOF is one direction for enhancing the applicability of FEM to room acoustic problems
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