Reconstruction of shapes and refractive indices from backscattering experimental data using the adaptivity
Journal article, 2014

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.

finite element method

coefficient inverse problem

globally convergent method


Larisa Beilina

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Nguyen Trung Thanh

The University of North Carolina at Charlotte

Michael V. Klibanov

The University of North Carolina at Charlotte

John Bondestam Malmberg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Inverse Problems

0266-5611 (ISSN)

Vol. 30 10 Art. no. 105007-

Subject Categories

Computational Mathematics


Basic sciences



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

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