An adaptive finite element method in reconstruction of coefficients in Maxwell’s equations from limited observations

Institute of Mathematics, Czech Academy of Sciences - Tập 61 - Trang 253-286 - 2016
Larisa Beilina1, Samar Hosseinzadegan2
1Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, Göteborg, Sweden
2Department of Signals and Systems Chalmers University of Technology Göteborg, Sweden

Tóm tắt

We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell’s system using limited boundary observations of the electric field in 3D. We derive a posteriori error estimates in the Tikhonov functional to be minimized and in the regularized solution of this functional, as well as formulate the corresponding adaptive algorithm. Our numerical experiments justify the efficiency of our a posteriori estimates and show significant improvement of the reconstructions obtained on locally adaptively refined meshes.

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Institute of Mathematics, Czech Academy of Sciences

Tập 61

253-286

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