Optimization approach for the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions from limited observations
For researchers in inverse problems, this work addresses a challenging parameter identification problem with theoretical stability via Carleman estimates, but the numerical validation is absent.
The paper tackles the simultaneous reconstruction of dielectric permittivity and magnetic permeability from limited boundary observations of the electric field in 3D Maxwell's system, using an optimization approach with hybrid finite element/difference methods. No concrete numerical results are provided.
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical stability for the problem is provided by the Carleman estimates. For the numerical computations the problem is formulated as an optimization problem and hybrid finite element/difference method is used to solve the parameter identification problem.