Numerical geometric acoustics

Abstract

We present a new approach to offline room acoustic modeling and simulation based on solving the eikonal equation, a nonlinear partial differential equation describing the arrival times of a high-frequency wavefront. We call the approach numerical geometric acoustics, since it combines some of the advantages of both numerical acoustics, where the acoustic wave equation or the Helmholtz equation are solved, and geometric acoustics, typically based on a variety of raytracing techniques. In our approach, reflection and diffraction effects are determined from boundary conditions connecting different eikonal problems generated by a recursion. This allows us to compute the multipath eikonal, a multivalued function parametrizing the arrival times of all acoustic rays propagating throughout a scene. Each branch of the multipath eikonal is computed by numerically solving the eikonal equation using a recently developed high-order semi-Lagrangian direct solver. This approach naturally encompasses spatially varying sound speeds. Our solver is compact and sufficiently high-order to allow us to transport the amplitude prefactor directly using paraxial raytracing. We discuss how to compute the acoustic parameter fields typical of precomputed room acoustic simulations used for virtual reality or games.