Dissipation-free and dispersion-optimized explicit time-domain finite element method for room acoustic modeling

Abstract

This paper presents a proposal for an efficient room acoustic solver with dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM), with investigation of its applicability for broadband room acoustic modeling from three numerical experiments. Recently, FEM-based room acoustic solvers have attracted great attention because of their strength in handling complex geometries. However, the development of higher-efficiency solvers is unavoidable to perform acoustic modeling of real-size rooms at kilohertz frequency with small discretization error: the dispersion error. The present paper first formulates a novel room acoustic solver with dissipation-free fourth-order accurate explicit TD-FEM using a three-step time integration method. A dispersion-optimized solver is further proposed in which dispersion error is minimized in the axial and diagonal directions at a specific frequency under given spatial resolution mesh or elements, by which the approximation capability at higher frequencies is enhanced without any additional computational cost. The performance of the optimized solver in broadband acoustic simulation using cubic elements is then examined in comparison with the original fourth-order accurate solver and the standard implicit TD-FEM. Finally, higher efficiency of the optimized solver is also demonstrated for acoustic simulation in a larger rectangular room discretized with rectangular and distorted hexahedral elements.