  The normal mode model is one of the most popular approaches for solving
underwater sound propagation problems. Among other methods, the finite
difference method is widely used in classic normal mode programs. In many
recent studies, the spectral method has been used for discretization. It is
generally more accurate than the finite difference method. However, the
spectral method requires that the variables to be solved are continuous in
space, and the traditional spectral method is powerless for a layered marine
environment. A Chebyshev-Tau spectral method based on domain decomposition is
applied to the construction of underwater acoustic normal modes in this paper.
In this method, the differential equation is projected onto spectral space from
the original physical space with the help of an orthogonal basis of Chebyshev
polynomials. A complex matrix eigenvalue / eigenvector problem is thus formed,
from which the solution of horizontal wavenumbers and modal functions can be
solved. The validity of the acoustic field calculation is tested in comparison
with classic programs. The results of analysis and tests show that compared
with the classic finite difference method, the proposed Chebyshev-Tau spectral
method has the advantage of high computational accuracy. In addition, in terms
of running time, our method is faster than the Legendre-Galerkin spectral
method.
