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An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations

Larisa Beilina (Institutionen för matematiska vetenskaper) ; Samar Hosseinzadegan (Institutionen för signaler och system, Biomedicinsk elektromagnetik)
Applications of Mathematics (0862-7940). Vol. 61 (2016), 3, p. 253-286.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Maxwell's system, coefficient inverse problem, Tikhonov functional, Lagrangian approach, a posteriori error estimate



Denna post skapades 2016-06-22. Senast ändrad 2016-06-27.
CPL Pubid: 238137

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)
Institutionen för signaler och system, Biomedicinsk elektromagnetik

Ämnesområden

Matematik

Chalmers infrastruktur