Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume
ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 49-66.

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.

DOI : 10.1051/cocv:2002071
Classification : 35J25, 35R30, 65R99
Mots clés : electromagnetic imaging, small inhomogeneities, numerical reconstruction algorithms 
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     title = {Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {49--66},
     publisher = {EDP-Sciences},
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Ammari, Habib; Moskow, Shari; Vogelius, Michael S. Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 49-66. doi : 10.1051/cocv:2002071. http://archive.numdam.org/articles/10.1051/cocv:2002071/

[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. | MR | Zbl

[2] S. Andrieux and A. Ben Abda, Identification of planar cracks by complete overdetermined data: Inversion formulae. Inverse Problems 12 (1996) 553-563. | MR | Zbl

[3] S. Andrieux, A. Ben Abda and M. Jaoua, On the inverse emerging plane crack problem. Math. Meth. Appl. Sci. 21 (1998) 895-907. | MR | Zbl

[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. II 327 (1999) 971-976. | Zbl

[5] E. Beretta, A. Mukherjee and M. Vogelius, Asymptotic formuli for steady state voltage potentials in the presence of conductivity imperfection of small area. ZAMP 52 (2001) 543-572. | MR | Zbl

[6] M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Preprint (2001). | MR | Zbl

[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. | MR

[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 Problems 14 (1998) 553-595. | Zbl

[9] I. Daubechies, Ten Lectures on Wavelets. SIAM, Philadelphia (1992). | MR | Zbl

[10] G.B. Folland, Introduction to Partial Differential Equations. Princeton University Press, Princeton (1976). | MR | Zbl

[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. | MR | Zbl

[12] S. He and V.G. Romanov, Identification of small flaws in conductors using magnetostatic measurements. Math. Comput. Simul. 50 (1999) 457-471. | MR

[13] M.S. Joshi and S.R. Mcdowall, Total determination of material parameters from electromagnetic boundary information. Pacific J. Math. (to appear). | MR | Zbl

[14] K. Miller, Stabilized numerical analytic prolongation with poles. SIAM J. Appl. Math. 18 (1970) 346-363. | MR | Zbl

[15] P. Ola, L. Païvärinta and E. Somersalo, An inverse boundary value problem in electrodynamics. Duke Math. J. 70 (1993) 617-653. | MR | Zbl

[16] M.S. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter 34 (2000) 723-748. | Numdam | MR | Zbl

[17] D. Volkov, An inverse problem for the time harmonic Maxwell Equations, Ph.D. Thesis. Rutgers University (2001).

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