On the computational efficiency of different waveguide mesh topologies for room acoustic simulation

Abstract

Room acoustic simulation using digital waveguide modeling requires three-dimensional waveguide meshes in order to represent fully the acoustic properties of the space. This paper presents a systematic analysis of four mesh topologies suggested in the literature: rectilinear, tetrahedral, cubic close-packed and octahedral. These mesh structures are compared from the standpoint of computational efficiency, bearing in mind specific issues that are important for room acoustic simulation. Each mesh topology offers a different compromise between spatial resolution, bandwidth, dispersion characteristics (including suitability for the application of dispersion-compensation techniques), computation time, memory requirements and implementation complexity.

Time-Domain Simulation of Directive Sources in 3-D Digital Waveguide Mesh-Based Acoustical Models

“…Several different 3-D mesh topologies exist for simulating wave propagation in volumes [37], [38]. Among these, the uniform rectilinear mesh topology provides a more attractive option in terms of the intuitive positioning of its junctions and the accuracy of numerical derivatives when the mesh density (i.e., the number of junctions per unit volume) is constant [39].…”

“…It also allows a more structured memory organization and has a well-documented prospect for software optimization and parallelization [40], [41]. Therefore, although it has higher directional dispersion errors [42] and a higher computational complexity [38] than other 3-D mesh topologies, uniformly sampled rectilinear topology is preferred for the examples in this paper. It should be noted that the methods proposed in this paper can be applied to other mesh topologies with slight modifications.…”

On the Accuracy of First-Order Numerical Derivatives in Multidimensional Digital Waveguide Mesh Topologies

“…For , the linear system of equations is underdetermined and a unique solution does not exist, while for , a unique solution exists if the matrix is not singular (i.e., the equations are linearly independent). For , which is also the case for regular mesh grids in two and three dimensions [9], the solution for can be obtained in the optimal sense as (9) where is the Moore-Penrose pseudoinverse of the matrix which is unique for each different positioning of sample points.…”

“…As with the 2-D case, for all topologies with . The reader is referred to [9] for the details of these topologies. Fig.…”

“…Another comparison is also made for the same mesh density in all topologies. Mesh densities for the 3-D topologies are given as , , , and , for cubic, tetrahedral, CCP, and BCC topologies, respectively [9].…”