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The numerical solution of an inverse periodic transmission problem
Author(s) -
Bruckner Gottfried,
Elschner Johannes
Publication year - 2004
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.588
Subject(s) - mathematics , lipschitz continuity , inverse problem , inverse , convergence (economics) , inverse scattering problem , mathematical analysis , boundary value problem , transmission (telecommunications) , numerical analysis , obstacle , periodic boundary conditions , geometry , computer science , telecommunications , political science , law , economics , economic growth
We consider the inverse problem of recovering a 2D periodic structure from scattered waves measured above and below the structure. We discuss convergence and implementation of an optimization method for solving the inverse TE transmission problem, following an approach first developed by Kirsch and Kress for acoustic obstacle scattering. The convergence analysis includes the case of Lipschitz grating profiles and relies on variational methods and solvability properties of periodic boundary integral equations. Numerical results for exact and noisy data demonstrate the practicability of the inversion algorithm. Copyright © 2004 John Wiley & Sons, Ltd.