Acoustic modeling in rectangular rooms with impedance using the finite element method with the Dirichlet-to-Neumann map

Abstract

Computational models of head-related transfer functions (HRTFs) are useful in investigating the effects of echoes and reverberations in enclosures. These models may be computed at relatively low cost by geometric methods, such as the image source method. However, geometric methods typically ignore several important physical effects, such as diffraction, which effect the fidelity of the resulting HRTF. On the other hand, methods based on solving the wave equation, such as the finite element method, include these effects but tend to be computationally expensive. This study represents a Dirichlet-to-Neumann (DtN) map which significantly reduces the costs associated with using the the finite element method for computing HRTFs in a rectangular room, by analytically eliminating empty regions of the room. The DtN map for rooms with realistic impedance boundary conditions is developed. This work represents an extension of our previous approach for sound-hard rooms [Y. Naka, A.A. Oberai, and B.G. Shinn-Cunningham, Proc. 18th International Congress on Acoustics, Vol. IV, pp. 2477–2480 (2004)]. [Work supported by AFOSR.]

A Review of Finite Element Methods for Room Acoustics

“…Naka et al [51] aimed to reduce the computational cost of solving FEM models of a rectangular room. This was achieved by reducing the size of the global stiffness matrix, by introducing an imaginary surface within the room on which a Dirichlet-to-Neumann (DtN) map boundary condition was imposed.…”

Finite-Element Method for Calculating the Sound Field in a Tank with Impedance Boundaries

“…ey analyzed the sound field of a scale model room with a well-defined geometry through experimental measurements and finite element methods. Naka et al [18] combined the geometric methods and finite element method to calculate the sound field in rooms with realistic impedance boundary conditions.…”