Accelerated sound propagation using an error-free Fourier method coupled with the spectral-element method

Simulating acoustics using numerical methods efficiently and accurately has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate the simulations using rectangular decomposition, enabling error-free propagation in the bulk of the domain consisting of air. We exploit the analytical solution to the wave equation calculated using the Fast Fourier Transform with near-optimal spatial and temporal discretizations satisfying the Nyquist criterium. Coupling with the spectral-element method near the boundaries results in a method capable of handling complex geometries with realistic boundaries, though with the caveat that additional errors and computational overhead may result from the interface. This talk will investigate the accuracy and efficiency of the proposed domain decomposition method compared to a spectral-element method running in the entire domain.