Compensation of staircase-induced boundary absorption errors in FDTD simulation

Finite-difference time-domain (FDTD) methods are popular for wave-based simulations because their regular grid enables highly efficient implementation, especially on parallel processing architectures. On the flip side, these methods exhibit errors caused by the staircase approximations that result when arbitrary boundary geometries are approximated on the fixed grid. Of particular concern in room acoustics is the staircasing of absorptive boundaries, as this has been shown to cause errors as large as 40% in computed reverberation times that do not reduce when the grid is refined. This paper analyses the effectiveness of a previously proposed compensation method that consists of modifying the admittance boundary conditions based on the staircased surface area. A theoretical analysis shows that for special boundary orientations the numerical reflection coefficient converges to the exact result at low frequencies. Numerical tests complement this analysis to show that the compensation yields accurate results at intermediate orientations as well. A spherical resonator case further demonstrates that a close match between numerically and analytically computed relaxation times is also obtained for curved boundaries.