Developments of parabolic equation method in the period of 2000–2016**Project supported by the Foundation of State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences (Grant No. SKLA201303) and the National Natural Science Foundation of China (Grant Nos. 11104044, 11234002, and 11474073).

Abstract

Parabolic equation (PE) method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underwater acoustics, it has been about 40 years, during which contributions to extending its capability has been continuously made. The most recent review paper surveyed the contributions made before 1999. In the period of 2000–2016, the development of PE method basically focuses on seismo-acoustic problems, three-dimensional problems, and realistic applications. In this paper, a review covering the contribution from 2000 to 2016 is given, and what should be done in future work is also discussed.