An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
Artikel i vetenskaplig tidskrift, 2016

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.

Tikhonov functional

coefficient inverse problem

Maxwell's system

a posteriori error estimate

Lagrangian approach

Författare

Larisa Beilina

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Samar Hosseinzadegan

Chalmers, Signaler och system, Signalbehandling och medicinsk teknik, Biomedicinsk elektromagnetik

Applications of Mathematics

0862-7940 (ISSN)

Vol. 61 253-286

Ämneskategorier

Matematik

DOI

10.1007/s10492-016-0131-0