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The Split-Step Padé-Fourier Solution

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Range-dependent ocean acoustics problems can be solved accurately and efficiently with the parabolic equation method. Several approaches have been developed, including the split-step Padé and split-step Fourier solutions. The split-step Padé solution is based on rational approximations and provides greater accuracy. The split-step Fourier solution is based on a linear approximation to the square root of an operator and provides greater efficiency for some high-frequency problems. The attributes of these approaches are combined to obtain the split-step Padé-Fourier solution, which provides a high level of accuracy and permits range steps of up to thousands of wavelengths for some high-frequency problems. This solution is obtained by multiplying and dividing by the exponential on which the split-step Fourier solution is based. One of the factors is implemented using the split-step Fourier solution. The other step is based on a rational approximation of an exponential function with a reduced oscillation rate, which permits larger range steps.
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Document Type: Research Article

Publication date: September 1, 2007

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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