Application of the Superposition Method with k-wave pseudo-spectral modelling

Finite-difference time-domain (FDTD) techniques are widely used to model the propagation of viscoelastic waves through heterogeneous media. The k-wave MATLAB toolbox is a popular tool for modeling of medical ultrasound simulations based on a pseudo-spectral decomposition [1]. The staircase effect is a specific source of error in both the k-wave and FDTD that arises when the boundary between different media does not align with the Cartesian grid used within numerical simulations. The superposition method is an approach that considerable reduces the staircasing effect in a Virieux staggered-grid FDTD scheme by combining multiple simulations with slightly different representations of the physical boundaries [2]. The superposition method can improve simulation accuracy by reducing diffractive scattering artifacts without the constraining computational resource requirements of high-resolution simulations.