A modal time-domain method for modeling dispersive and dissipative linear waves

A modal time-domain method is developed for simulating linear dispersive and dissipative waves in 3D geometries. Two of the principle challenges in modeling large acoustic systems are fitting models into computer memory and managing numerical wave speed errors; both prevent modeling of large problems and high frequencies. To address these issues, a framework is developed for solving linear wave equations on a structured subdivided domain using exact frequency-dependent time integration. From the perspective of modeling sound in rooms, the method is shown to accurately capture propagation losses due to air absorption, dispersive bending waves in panels, lossy propagation in porous media, and dispersionless propagation over large distances. This approach enjoys exact time integration for many PDE, but such accuracy comes at the cost of highly-structured grids and non-trivial boundary conditions. Advantages and shortcomings are discussed relative to problems of practical size and interest.