The numerical solution of an inverse periodic transmission problem

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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2005-05, Vol.28 (7), p.757-778
Main Authors: Bruckner, Gottfried, Elschner, Johannes
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
diffraction grating
Exact sciences and technology
Integral equations
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
optimization method
profile reconstruction
Sciences and techniques of general use
TE transmission problem
Tikhonov regularization
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.588