FDTD (Finite-Difference Time-Domain)

Finite-Difference Time-Domain (FDTD) is a numerical wave-based simulation method that solves the acoustic wave equation by discretizing space and time into a grid. At each time step, pressure and velocity values are updated at every grid point based on neighboring values. FDTD captures all wave phenomena including diffraction, interference, room modes, and scattering, making it accurate across the full frequency range including low frequencies where ray-based methods fail. The computational cost is extremely high: the grid spacing must be at least 6–10 points per wavelength, so simulating frequencies up to 1 kHz in a 100 m³ room requires millions of grid points and hours of computation. FDTD is primarily used for research, small-room low-frequency analysis, and validating simpler models. It is increasingly accessible through GPU acceleration and is valuable for studio design, room mode prediction, and complex geometry analysis where geometric methods are inadequate.