Singularity of scattering and Dirichlet-to-Neumann operator symbols in elliptic wave propagation models

Ji Hun Yoon, Jeong-Hoon Kim, Jinnam Jo

Research output: Contribution to journalArticle

Abstract

Combining wave field decomposition, invariant imbedding and general phase theory can reformulate the ill-posed elliptic wave propagation problems into the exact, well-posed, one-way problems. As a main focus in the direct and inverse analysis of this approach, the singularity structure (turning points, focal points, cusps, kinks and poles) of the scattering and Dirichlet-to-Neumann operator symbols are presented and analysed in the transversely homogeneous limit. A specific 2D example is provided with numerical results.

Original languageEnglish
Pages (from-to)651-675
Number of pages25
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume80
Issue number3
DOIs
Publication statusPublished - 2015 Sep 1

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Wave propagation
Wave Propagation
Dirichlet
Poles
Scattering
Singularity
Decomposition
Invariant Imbedding
Inverse Analysis
Turning Point
Kink
Cusp
Operator
Pole
Decompose
Numerical Results
Model

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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abstract = "Combining wave field decomposition, invariant imbedding and general phase theory can reformulate the ill-posed elliptic wave propagation problems into the exact, well-posed, one-way problems. As a main focus in the direct and inverse analysis of this approach, the singularity structure (turning points, focal points, cusps, kinks and poles) of the scattering and Dirichlet-to-Neumann operator symbols are presented and analysed in the transversely homogeneous limit. A specific 2D example is provided with numerical results.",
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AB - Combining wave field decomposition, invariant imbedding and general phase theory can reformulate the ill-posed elliptic wave propagation problems into the exact, well-posed, one-way problems. As a main focus in the direct and inverse analysis of this approach, the singularity structure (turning points, focal points, cusps, kinks and poles) of the scattering and Dirichlet-to-Neumann operator symbols are presented and analysed in the transversely homogeneous limit. A specific 2D example is provided with numerical results.

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