Implementation of surface impedance boundary conditions in the split-step 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. This allows use of fast Fourier transform (FFT) methods to implement the SSFPE algorithm. In many cases, however, the surface boundary condition is of the mixed or impedance type which precludes use of simple FFTs. In this talk, generalizations of the SSFPE algorithm will be discussed that use a novel fast radiation transform (FRT). The FRT allows explicit incorporation of complex surface impedance boundary conditions into the SSFPE algorithm, while still retaining computational efficiency. Illustrative examples that use this new method will be shown.