Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.