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- Jung, Chang-Yeol
- Numerical Analysis Lab.
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ASYMPTOTIC ANALYSIS OF THE SCATTERING PROBLEM FOR THE HELMHOLTZ EQUATIONS WITH HIGH WAVE NUMBERS
- Author(s)
- Bouche, Daniel, Hong, Youngjoon, Jung, Chang-Yeol
- Issued Date
- 2017-03
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.37, no.3, pp.1159 - 1181
- Abstract
- We study the asymptotic behavior of the two dimensional Helmholtz scattering problem with high wave numbers in an exterior domain, the exterior of a circle. We impose the Dirichlet boundary condition on the obstacle, which corresponds to an incidental wave. For the outer boundary, we consider the Sommerfeld conditions. Using a polar coordinates expansion, the problem is reduced to a sequence of Bessel equations. Investigating the Bessel equations mode by mode, we find that the solution of the scattering problem converges to its limit solution at a specific rate depending on k.
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- ISSN
- 1078-0947
- Keyword (Author)
- Electromagnetism, acoustics, Helmholtz equations, scattering problem, asymptotic analysis
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