Abstract
A numerical method is developed for solving the two-dimensional Helmholtz equation in a region bounded by a flat top and a curved bottom. A local orthogonal transformation is first used to flatten the curved bottom of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method for discretizing the range variable and a truncated local eigenfunction expansion for approximating the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides.
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