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Wide-angle one-way wave equations.

L Halpern1, L N Trefethen

  • 1Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France.

The Journal of the Acoustical Society of America
|October 1, 1988
PubMed
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This study introduces new coefficients for one-way wave equations, improving wide-angle behavior for applications in acoustics and geophysics. These novel approximants offer enhanced performance over traditional methods.

Area of Science:

  • Computational physics
  • Applied mathematics
  • Wave propagation modeling

Background:

  • One-way wave equations model wave propagation in specific directions.
  • Applications include underwater acoustics, geophysics, and numerical boundary conditions.
  • Design relies on rational function approximation of (1-s^2)^1/2.

Purpose of the Study:

  • To present new coefficients for one-way wave equations.
  • To improve wide-angle behavior compared to standard Padé approximations.
  • To offer alternative approximants for enhanced wave propagation modeling.

Main Methods:

  • Approximation of the function (1-s^2)^1/2 on [-1,1] using rational functions.
  • Development of coefficients for L2 and L-infinity norm classes.

Related Experiment Videos

  • Consideration of alternative approximant classes for improved performance.

    • Main Results:

    • Coefficients for L2 and L-infinity approximants are provided.
    • Alternative approximants demonstrate superior wide-angle behavior.
    • The study builds upon established well-posedness results for these equations.

    Conclusions:

    • The presented coefficients offer improved wide-angle capabilities for one-way wave equations.
    • These findings enhance modeling in fields like underwater acoustics and geophysics.
    • The work provides valuable tools for numerical wave propagation simulations.