An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
This work addresses the challenging inverse problem of coefficient reconstruction in Maxwell's equations for electromagnetic imaging, offering an adaptive approach that improves reconstruction quality.
The paper proposes an adaptive finite element method for simultaneously reconstructing dielectric permittivity and magnetic permeability in Maxwell's equations from limited boundary observations. Numerical experiments demonstrate significant improvement in reconstructions on locally adaptively refined meshes.
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 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.