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Two-dimensional acoustic scattering, conformal mapping, and the Rayleigh hypothesis
1Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado 80401-1887, USA. pamartin@mines.edu
The Journal of the Acoustical Society of America
|October 9, 2012
Summary
Investigating conformal mapping methods for two-dimensional scattering problems reveals their convergence depends on a mapped Rayleigh hypothesis. These methods offer no advantage over existing techniques using circular-cylindrical wavefunctions.
Area of Science:
- Electromagnetics and Acoustics
- Computational Physics
Background:
- Two-dimensional scattering problems are crucial in various physics and engineering fields.
- Established methods often utilize expansions in circular-cylindrical wavefunctions.
Purpose of the Study:
- To investigate the efficacy of conformal mapping methods for solving 2D scattering problems.
- To analyze the convergence properties and advantages of these novel approaches.
Main Methods:
- The study employs conformal mapping techniques to transform the scattering domain.
- Convergence analysis is performed, focusing on a mapped version of the Rayleigh hypothesis.
Main Results:
- The convergence of conformal mapping methods is demonstrated to be contingent upon a mapped Rayleigh hypothesis.
- No significant advantages were found compared to traditional methods.
Conclusions:
- Conformal mapping methods do not surpass established techniques for 2D scattering problems.
- The reliance on a mapped Rayleigh hypothesis limits their practical utility.
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