Modeling Specular and Diffuse Reflection Sound Fields in Enclosures with an Energy-Intensity Boundary Element Method

Steady-state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics that are orthogonal on the half-space. The amplitudes of these harmonics are determined by a Lagrange multiplier method to satisfy the energy conservation integral constraint. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Monotonic convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. The method is very computationally efficient. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and a broadband image method, demonstrating high accuracy. The method of absorption scaling is verified for complicated 3-D cases, and showing that the spatial variation in rooms is largely determined by source position and the relative distribution of absorption, but not the overall absorption level.