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VALIDITY OF ONE-WAY MODELS IN THE WEAK RANGE DEPENDENCE LIMIT

JIANXIN ZHU

Department of Mathematics, Zhejiang University, Hangzhou 310027, China

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and

YA YAN LU

Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China

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https://doi.org/10.1142/S0218396X0400216XCited by:11 (Source: Crossref)

Abstract

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.

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