Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume

Habib Ammari; Shari Moskow; Michael S. Vogelius

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 9, page 49-66
  • ISSN: 1292-8119

Abstract

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In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.

How to cite

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Ammari, Habib, Moskow, Shari, and Vogelius, Michael S.. "Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 49-66. <http://eudml.org/doc/90708>.

@article{Ammari2010,
abstract = { In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities. },
author = {Ammari, Habib, Moskow, Shari, Vogelius, Michael S.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Electromagnetic imaging; small inhomogeneities; numerical reconstruction algorithms.; electromagnetic imaging; numerical reconstruction algorithms},
language = {eng},
month = {3},
pages = {49-66},
publisher = {EDP Sciences},
title = {Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume},
url = {http://eudml.org/doc/90708},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Ammari, Habib
AU - Moskow, Shari
AU - Vogelius, Michael S.
TI - Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 49
EP - 66
AB - In this paper we discuss the approximate reconstruction of inhomogeneities of small volume. The data used for the reconstruction consist of boundary integrals of the (observed) electromagnetic fields. The numerical algorithms discussed are based on highly accurate asymptotic formulae for the electromagnetic fields in the presence of small volume inhomogeneities.
LA - eng
KW - Electromagnetic imaging; small inhomogeneities; numerical reconstruction algorithms.; electromagnetic imaging; numerical reconstruction algorithms
UR - http://eudml.org/doc/90708
ER -

References

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  1. H. Ammari, M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell Equations. J. Math. Pures Appl.80 (2001) 769-814.  Zbl1042.78002
  2. S. Andrieux and A. Ben Abda, Identification of planar cracks by complete overdetermined data: Inversion formulae. Inverse Problems12 (1996) 553-563.  Zbl0858.35131
  3. S. Andrieux, A. Ben Abda and M. Jaoua, On the inverse emerging plane crack problem. Math. Meth. Appl. Sci.21 (1998) 895-907.  Zbl0916.35129
  4. H.D. Bui, A. Constantinescu and H. Maigre, Diffraction acoustique inverse de fissure plane : solution explicite pour un solide borné. C. R. Acad. Sci. Paris Sér. II327 (1999) 971-976.  Zbl0966.74038
  5. E. Beretta, A. Mukherjee and M. Vogelius, Asymptotic formuli for steady state voltage potentials in the presence of conductivity imperfection of small area. ZAMP52 (2001) 543-572.  Zbl0974.78006
  6. M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Preprint (2001).  Zbl1016.65079
  7. A.P. Calderon, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics. Soc. Brasileira de Matemática, Rio de Janeiro (1980) 65-73.  
  8. D.J. Cedio-Fengya, S. Moskow and M.S. Vogelius, Identification of conductivity inperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems14 (1998) 553-595.  Zbl0916.35132
  9. I. Daubechies, Ten Lectures on Wavelets. SIAM, Philadelphia (1992).  Zbl0776.42018
  10. G.B. Folland, Introduction to Partial Differential Equations. Princeton University Press, Princeton (1976).  Zbl0325.35001
  11. A. Friedman and M. Vogelius, Identification of Small Inhomogeneities of Extreme Conductivity by Boundary Measurements: A Theorem on Continuous Dependence. Arch. Rational Mech. Anal.105 (1989) 299-326.  Zbl0684.35087
  12. S. He and V.G. Romanov, Identification of small flaws in conductors using magnetostatic measurements. Math. Comput. Simul.50 (1999) 457-471.  
  13. M.S. Joshi and S.R. McDowall, Total determination of material parameters from electromagnetic boundary information. Pacific J. Math. (to appear).  Zbl1012.78012
  14. K. Miller, Stabilized numerical analytic prolongation with poles. SIAM J. Appl. Math.18 (1970) 346-363.  Zbl0211.19303
  15. P. Ola, L. Païvärinta and E. Somersalo, An inverse boundary value problem in electrodynamics. Duke Math. J.70 (1993) 617-653.  Zbl0804.35152
  16. M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. ESAIM: M2AN34 (2000) 723-748.  Zbl0971.78004
  17. D. Volkov, An inverse problem for the time harmonic Maxwell Equations, Ph.D. Thesis. Rutgers University (2001).  

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