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PubMed · 3198873

Wide-angle one-way wave equations.

L Halpern·L N Trefethen
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Abstract

A one-way wave equation, also known as a paraxial or parabolic wave equation, is a differential equation that permits wave propagation in certain directions only. Such equations are used regularly in underwater acoustics, in geophysics, and as energy-absorbing numerical boundary conditions. The design of a one-way wave equation is connected with the approximation of (1-s2)1/2 on [-1,1] by a rational function, which has usually been carried out by Padé approximation. This article presents coefficients for L2, L infinity, and other alternative classes of approximants that have better wide-angle behavior. For theoretical results establishing the well posedness of these wide-angle equations, see the work of Trefethen and Halpern ["Well-posedness of one-way wave equations and absorbing boundary conditions," Math. Comput. 47, 421-435 (1986)].

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AcousticsMathematicsJournal ArticleResearch Support, Non-U.S. Gov'tResearch Support, U.S. Gov't, Non-P.H.S.

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L Halpern, L N Trefethen. 1988. Wide-angle one-way wave equations.. https://doi.org/10.1121/1.396586

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