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Rigorous numerics for the Pekeris problem.

Richard B Evans1

  • 1Retired, 99F Hugo Road, North Stonington, Connecticut 06359, USA rbevans@99main.com.

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Summary
This summary is machine-generated.

Researchers determined the required truncation depth for accurate acoustic field approximations in attenuating Pekeris waveguides. This method uses rigorous numerics and a contraction mapping, avoiding the need to compute the full waveguide field limit.

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Area of Science:

  • Acoustics
  • Waveguide Theory
  • Numerical Analysis

Background:

  • The acoustic field in an attenuating Pekeris waveguide is mathematically defined as the limit of a truncated waveguide.
  • Accurate approximations are crucial for practical applications in underwater acoustics and geophysics.

Purpose of the Study:

  • To develop a method for determining the necessary truncation depth for accurate acoustic field approximations in attenuating Pekeris waveguides.
  • To establish a rigorous numerical approach for error estimation without computing the full field limit.

Main Methods:

  • Rigorous numerical computations were employed.
  • A contraction mapping in a specifically formulated norm, based on Rayleigh's theorem, was utilized.
  • Error determination was based solely on approximations within the truncated waveguide.

Main Results:

  • The rate of convergence for the acoustic field was determined.
  • A contraction mapping formulation was established to calculate the required truncation depth for a given error tolerance.
  • The method allows for precise error control in approximating the waveguide field.

Conclusions:

  • The study provides a practical method to determine the truncation depth for accurate acoustic field approximations in attenuating Pekeris waveguides.
  • This approach enhances computational efficiency by avoiding the calculation of the infinite waveguide limit.
  • The findings are significant for numerical modeling in acoustic wave propagation.