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Reconstruction of discontinuous parameters in a second order impedance boundary operator

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HAL-INRIA
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  • [Info.Info-Na] Computer Science [Cs]/Numerical Analysis [Cs.Na]
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Abstract

We consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Khon-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of unknown number of discontinuity points.

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