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

Ji Hun Yoon; Jeong Hoon Kim; Jinnam Jo

doi:10.1093/imamat/hxu006

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

Ji Hun Yoon, Jeong Hoon Kim, Jinnam Jo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	651-675
Number of pages	25
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	80
Issue number	3
DOIs	https://doi.org/10.1093/imamat/hxu006
Publication status	Published - 2015 Sep 1

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© 2014 The authors.

All Science Journal Classification (ASJC) codes

Applied Mathematics

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

Abstract

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