Otilio Rojas

Barcelona Supercomputing Center, Spain 

A Pseudo-Spectral Time-Domain (PSTD) method to model the propagation of acoustic waves on materials exhibiting frequency-dependent power law absorption and dispersion is introduced. We first analyze the physical dispersion of a material imitating biological tissue in the frequency ranges typical of ultrasound explorations using a lossy wave equation given in the literature. Second, we develop a von Neumann analysis of our PSTD scheme that quantifies the dependence of the numerical stability on the material parameters and the time step but also establishes the contribution of the spatial step to this numerical property. This contribution is singular and not observed in similar results derived for the standard linear lossless acoustic case. Next, we present a couple of numerical experiments whose results allow us to validate analytical stability bounds and quantify numerical dissipation and dispersion