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

Larisa Beilina; Samar Hosseinzadegan

Applications of Mathematics (2016)

  • Volume: 61, Issue: 3, page 253-286
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Beilina, Larisa, and Hosseinzadegan, Samar. "An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations." Applications of Mathematics 61.3 (2016): 253-286. <http://eudml.org/doc/276982>.

@article{Beilina2016,
abstract = {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.},
author = {Beilina, Larisa, Hosseinzadegan, Samar},
journal = {Applications of Mathematics},
keywords = {Maxwell's system; coefficient inverse problem; Tikhonov functional; Lagrangian approach; a posteriori error estimate},
language = {eng},
number = {3},
pages = {253-286},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations},
url = {http://eudml.org/doc/276982},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Beilina, Larisa
AU - Hosseinzadegan, Samar
TI - An adaptive finite element method in reconstruction of coefficients in Maxwell's equations from limited observations
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 253
EP - 286
AB - 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.
LA - eng
KW - Maxwell's system; coefficient inverse problem; Tikhonov functional; Lagrangian approach; a posteriori error estimate
UR - http://eudml.org/doc/276982
ER -

References

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