Modeling nonlinear wave propagation on nonuniform grids using a mapped k-space pseudospectral method

Simulating the propagation of nonlinear ultrasound waves is computationally difficult because of the dense grids needed to capture high-frequency harmonics. Here, a mapped k-space pseudospectral method is presented which allows the use of nonuniform grid spacings. This enables grid points to be clustered around steep regions of the wave field. Compared with using a uniform grid, this significantly reduces the total number of grid points needed for accurate simulations. Two methods for selecting a suitable nonuniform grid mapping are discussed.