The PSTD algorithm: A time-domain method combining the pseudospectral technique and perfectly matched layers

Abstract

Simulations of underwater acoustic wave propagation require solutions for large-scale multidimensional problems. The traditional finite-difference time-domain (FDTD) method needs a fine discretization of 8–20 cells per wavelength in order to give accurate results. On the other hand, the pseudospectral method, even though efficient, suffers from the wraparound effect due to the use of discrete Fourier transform. This effect severely limits the applications of the pseudospectral method to large-scale problems. Hence, a popular way of simulating underwater acoustic wave propagation is to use the parabolic equation (PE) methods which neglect backscattering. In this work, Berenger’s perfectly matched layers (PML) are used in the pseudospectral method to eliminate the wraparound effect. To achieve a high accuracy, this method requires only two cells per wavelength which is dictated by the Nyquist sampling theorem. As a result, it can solve at least 64 times larger 3-D problems than the FDTD method with the same requirement in computer memory and CPU time. Hence, full-wave solutions of long-range underwater acoustic wave propagation become possible. Numerous simulations show the superiority of the PSTD method for large-scale problems. [Work supported by a Presidential Early Career Award for Scientists and Engineers through EPA and by Sandia National Laboratories.]