PhD Proposal: Numerical Geometric Acoustics

Large-scale, physically modelled sound propagation has received recent attention as a viable means of simulating realistic architectural and environmental acoustics. Acoustics are treated as an asset to be baked offline and used by soft real-time applications like games. Point-to-point room impulse responses (RIRs) can be computed between many source and receiver locations and convolved with dry sound effects online as a person navigates through an environment to give a realistic impression of the space. Existing approaches belong to either the realm of numerical acoustics, where the wave physics are simulated directly, or geometric acoustics, where raytracing methods are applied. The former is appropriate for low to medium frequency problems, while the latter works well for high frequency problems.We propose a new approach based on the direct solution of the high frequency (WKB) approximation of the Helmholtz equation defined on a complicated domain, such as a large and intricate 3D environment, typical of a game or virtual environment. This allows us to recover the complete geometric acoustic field, including multiple arrivals. The crux of our method is a compact, high-order, semi-Lagrangian direct solver for the eikonal equation, which describes the phase of rays propagating in an environment. We couple this solver with techniques from physical optics and high frequency acoustic diffraction theory to compute the phase and amplitude of all rays, accounting for reflection and diffraction.Since our efforts are focused on large-scale acoustic modeling, applying our algorithms to realistic (large) problems is crucial. We present additional results related to modeling sound propagation in built environments, including how to practically adapt our solver to large, unstructured tetrahedron meshes. We show how we can use the eikonal equation itself to adaptively place sampling probes. Additionally, we describe how our work relates to existing time-domain algorithms, and a design for a memory-efficient parallel pipelined encoder.We refer to our combined set of techniques as numerical geometric acoustics, and our high-order method for solving the eikonal equation as a jet marching method. We discuss how to design jet marching methods for more general static Hamilton-Jacobi equations, of which the eikonal equation is a special case. Furthermore, our numerical algorithms constitute a development that stands independently of the room acoustics thrust of our proposal; in particular, they relate to the broader field of Eulerian geometric optics. We discuss how our results complement and improve on existing results in this field.Examining Committee:

Chair: Dr. Maria Cameron Dept rep: Dr. Ming Lin Members: Dr. Ramani Duraiswami Dr. Howard Elman