Impedance boundary conditions for pseudo-spectral time-domain methods in room acoustics

The pseudo-spectral time-domain (PSTD) method is an alternative time-marching method to classical leapfrog finite difference schemes in the simulation of wave-like propagating phenomena. It is based on the fundamentals of the Fourier transform to compute the spatial derivatives of hyperbolic differential equations. Therefore, it results in an isotropic operator that can be implemented in an efficient way for room acoustics simulations. However, one of the first issues to be solved consists on modeling wall absorption. Unfortunately, there are no references in the technical literature concerning to that problem. In this paper, assuming real and constant locally reacting impedances, several proposals to overcome this problem are presented, validated and compared to analytical solutions in different scenarios.