Non-Uniform Time-Stepping in k-Space Pseudospectral Time Domain Models of Acoustic Propagation

Non-uniform time stepping in acoustic propagation models can be used to preserve accuracy or reduce computational cost for an acoustic simulation with a wave front propagating through a domain with both heterogeneous and homogenous regions, such as for a simulation of breast ultrasound tomography. The k-space correction already exist within the literature to remove numerical dispersion caused by the time stepping procedure in pseudo-spectral time domain models, but requires a uniform time step. Here we expand this correction to be able to account for a non-uniform time stepping method and illustrate the potential advantages and considerations.