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Validity of one-way models in the weak range dependence limit. (English) Zbl 1256.76067

Summary: Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be further approximated by various one-way models used in underwater acoustics. An operator marching method based on the Dirichlet-to-Neumann map and a local orthogonal transform is used to solve the Helmholtz equation.

MSC:

76Q05 Hydro- and aero-acoustics
65N99 Numerical methods for partial differential equations, boundary value problems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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