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Adaptive finite element method for a coefficient inverse problem for Maxwell’s system. (English) Zbl 1223.78010
Summary: We consider a coefficient inverse problem for Maxwell’s system in 3-D. The coefficient of interest is the dielectric permittivity function. Only backscattering single measurement data are used. The problem is formulated as an optimization problem. The key idea is to use the adaptive finite element method for the solution. Both analytical and numerical results are presented. Similar ideas for inverse problems for the complete time dependent Maxwell’s system were not considered in the past.

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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