Ultrasound wave propagation through rough interfaces: Iterative methods

Two iterative methods for the calculation of acoustic transmission through a rough interface between two media are compared. The methods employ a continuous version of the conjugate gradient technique. One method is based on plane-wave expansions and the other on boundary integral equations and Green’s functions. A preconditioner is presented which improves the convergence for spectra that include evanescent modes. The methods are compared with regard to computational efficiency, rate of convergence, and residual error. The sound field differences are determined for a focused ultrasound beam distorted by surfaces having a Gaussian roughness spectrum. The differences are evaluated from the root-mean-square differences on the rough surface and in the focal plane.