About an inverse electromagnetic coefficient problem: uniqueness with partial boundary data and quasi-reversibility method for data completion
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This paper deals with two questions relative to the inverse coefficient problem of recovering the electric permittivity and conductivity of a medium from partial boundary data at a fixed frequency. The underlying model is the time-harmonic Maxwell equations in the electric field. First, an identifiability result is proved for partial boundary data without restrictive conditions on the inaccessible part of the boundary. The second issue that is addressed, is the data completion problem on the inaccessible part of the boundary. The quasi-reversibility method is studied, and different mixed formulations are proposed. Well-posedness and convergence results are proved. Various two- and three dimensional numerical simulations attest the efficiency of the method, in particular for noisy data.
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