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Inverse scattering from an open arc
Author(s) -
Kress Rainer
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180403
Subject(s) - mathematics , inverse scattering problem , mathematical analysis , arc (geometry) , boundary value problem , plane wave , inverse scattering transform , operator (biology) , boundary (topology) , scattering , inverse problem , completeness (order theory) , differentiable function , integral equation , inverse , field (mathematics) , geometry , optics , physics , pure mathematics , biochemistry , chemistry , repressor , transcription factor , gene
Abstract A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound‐soft or perfectly conducting arc from a knowledge of the far‐field pattern for the scattering of time‐harmonic plane waves. Fréchet differentiability with respect to the boundary is shown for the far‐field operator, which for a fixed incident wave maps the boundary arc onto the far‐field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.