Implementation of generalized impedance boundary condition in the split‐step Fourier parabolic equation

Abstract

The parabolic wave equation (PE) is a powerful numerical method for computing the full‐wave complex acoustic pressure field in range‐dependent environments. The split‐step Fourier PE algorithm (SSFPE) of Hardin and Tappert provides a very efficient computational implementation of PE when the surface boundary condition is of the Dirichlet or Neumann form, and when the solution decays sufficiently with depth. This allows use of fast Fourier transform (FFT) methods to implement the SSFPE algorithm. Typically the infinite domain radiation condition is approximated on a finite calculation grid by employing an artificial absorber or sponge. In some cases involving strong bottom interaction, however, the required absorber region may be quite large. This results in an increased computational load. A new method for truncating the absorber region will be described that is based upon splitting the PE field into two components that are in turn propagated on different vertical wave‐number grids. Illustrative examples that use this new method will be shown. [Work supported by NRaD IR program.]