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Wide-angle one-way wave equations
1Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France.
The Journal of the Acoustical Society of America
|October 1, 1988
Summary
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.
- 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.