Exploration of efficient numerical integration rule for wideband room-acoustics simulations by plane-wave-enriched finite-element method

In this study, we assessed the reduction in the computational costs of a room-acoustics solver by the partition of unity finite-element method (PUFEM), particularly addressing the element matrix construction process with numerical integration rules. The PUFEM enriches the approximation of sound fields by incorporating a general solution of the Helmholtz equation into shape functions. Plane wave enrichment is applied herein. In plane-wave-enriched FEM, the construction of element matrices using a high-order Gauss–Legendre quadrature is the main numerical operation with a long computational time. To reduce the computational time of the room-acoustics solver with plane-wave-enriched FEM, in this report, we describe our exploration of efficient integration rules via an ideal plane wave propagation problem in a duct. We present two integration rules: a well-used existing rule extended to the low-frequency range and another derived by the linear regression of the relationship between the number of wavelengths included in each element and the minimum number of integration points required for solution convergence. Numerical results revealed that both rules produce accurate frequency responses in a broad frequency range. However, the rule obtained by linear regression outperforms the extended rule.