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Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity

Larisa Beilina (Institutionen för matematiska vetenskaper, matematik) ; Nguyen Trung Thanh ; Michael V. Klibanov ; John Bondestam Malmberg (Institutionen för matematiska vetenskaper, matematik)
Inverse Problems (0266-5611). Vol. 30 (2014), 10, p. Art. no. 105007.
[Artikel, refereegranskad vetenskaplig]

We consider the inverse problem of the reconstruction of the spatially distributed dielectric constant epsilon(r)(x), x is an element of R-3, which is an unknown coefficient in the Maxwell's equations, from time-dependent backscattering experimental radar data associated with a single source of electric pulses. The refractive index is n(x) = root epsilon(r)(x). The coefficient epsilon(r)(x) is reconstructed using a two-stage reconstruction procedure. In the first stage an approximately globally convergent method proposed is applied to get a good first approximation of the exact solution. In the second stage a locally convergent adaptive finite element method is applied, taking the solution of the first stage as the starting point of the minimization of the Tikhonov functional. This functional is minimized on a sequence of locally refined meshes. It is shown here that all three components of interest of targets can be simultaneously accurately imaged: refractive indices, shapes and locations.

Nyckelord: coefficient inverse problem; finite element method; globally convergent method

Preprint in fulltext: http://www.math.chalmers.se/Math/Research/Preprints/2014/9.pdf

Denna post skapades 2014-04-29. Senast ändrad 2016-06-27.
CPL Pubid: 197267


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University 2014:9