Fast computation of wave propagation in the open acoustical waveguide with a curved interface

In ocean acoustics, the ocean is considered simply as an open waveguide with a curved interface. To compute the wave propagation in the waveguide, firstly a local orthogonal coordinate transform and an equation transform are applied; secondly a perfectly matched layer (PML) is used to terminate the open waveguide to a bounded one. In this way, the curved interface is turned to a flat one and the equation is also changed to another form in the bounded domain. Based the Dirichlet-to-Neumann (DtN) map, the boundary value problem is reduced to an initial problem. In this paper, a new marching method is provided to solve the initial problem fast. Numerical results show that our treatment is feasible and more efficient.