An efficient enhancement of finite‐difference implementations for solving parabolic equations

Abstract

The parabolic approximation method is widely recognized as useful for accurately analyzing and predicting sound transmission intensity in diverse ocean environments. One reason for its attractiveness is that solutions are marched in range, thereby avoiding the large internal storage requirements when using the full wave equation. Present finite‐difference implementations employ a range step size that is prescribed by either the user or the code and that remains fixed for the duration of the computation. An algorithm is presented in which the range step is adaptively selected by a procedure within a version of the implicit finite‐difference (IFD) implementation of the parabolic approximation. An error indicator is computed at each range step, and its value is compared to an error tolerance window that is readily specified by the user. If the error indicator falls outside this window, a new range step size is computed and used until the error indicator again leaves the tolerance window. Furthermore, for a given tolerance, this algorithm generates a range step size that is optimal in a specified sense and that often leads to large decreases in run time. Additional related modifications to the IFD implementations are discussed. Several examples are presented that illustrate the efficacy of the enhanced algorithm.