Optimised implicit methods for audio rate wave-based acoustic simulation

Wave-based room acoustic computation at an audio rate (i.e., covering the complete range of audible frequencies) is computationally intensive. There is thus a great incentive to develop simulation methods that allow for "accurate" simulation at the lowest possible computational cost, taking into account requirements for massively parallel implementation. Though often formal measures of order of accuracy are employed, in this paper, we examine the optimisation of a locally-defined implicit family of schemes against wideband measures of accuracy, based on the minimisation of numerical dispersion over a specified frequency range. The resulting optimised scheme is defined over a Cartesian grid, and allows performance gains over standard schemes (such as the basic rectilinear scheme, or schemes defined over face-centered cubic grids, and other implicit designs presented in the literature). Numerical stability conditions are easily formulated, and can be built into the optimisation, alongside the computational cost of linear system solution. Simulation results and comparisons of computation times against other known methods are presented.