Extension of a spectral time-stepping domain decomposition method for dispersive and dissipative wave propagation

For time-domain modeling based on the acoustic wave equation, spectral methods have recently demonstrated promise. This letter presents an extension of a spectral domain decomposition approach, previously used to solve the lossless linear wave equation, which accommodates frequency-dependent atmospheric attenuation and assignment of arbitrary dispersion relations. Frequency-dependence is straightforward to assign when time-stepping is done in the spectral domain, so combined losses from molecular relaxation, thermal conductivity, and viscosity can be approximated with little extra computation or storage. A mode update free from numerical dispersion is derived, and the model is confirmed with a numerical experiment.