Anisotropic polarization tensors and detection of an anisotropic inclusion

SIAM Journal on Applied Mathematics

Volumn 63, Issue 4, 2003, Pages 1276-1291

  Kang, Hyeonbae ^a   Kim, Eunjoo ^a   Kim, Kyoungsun ^a  

^a Seoul National University   (South Korea)

Author keywords

Anisotropic conductivity; Anisotropic polarization tensor; Asymptotic expansion; Electrical impedance tomography; Far field

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC IMPEDANCE TOMOGRAPHY; POLARIZATION;

ASYMPTOTIC EXPANSION;

ANISOTROPY;

EID: 0042977381     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613990240619X     Document Type: Article

References (19)

1. H. AMMARI AND H. KANG, High-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of conductivity inhomogeneities of small diameter, SIAM J. Math. Anal., to appear.
2. H. AMMARI AND H. KANG, Properties of generalized polarization tensors, Multiscale Model. Simul, to appear.
3. H. AMMARI, S, MOSKOW, AND M. VOGELIUS, Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter, ESAIM: Control Optim. Calc. Var., to appear.
4. H. AMMARI AND J. K. SEO, A New Formula for the Reconstruction of Conductivity Inhomogeneities, Adv. Appl. Math., to appear.
5. M. BRÜHL, M. HANKE, AND M. VOGELIUS, A Direct Impedance Tomography Algorithm for Locating Small Inhomogeneities, Numer. Math., to appear.
6. D. J. CEDIO-FENGYA, S. MOSKOW, AND M. VOGELIUS, Identification of conductivity imperfections of small diameter by boundary measurements: Continuous dependence and computational reconstruction, Inverse Problems, 14 (1998), pp. 553-595.
7. L. ESCAURIAZA AND J. K. SEO, Regularity properties of solutions to transmission problems, Trans. Amer. Math. Soc., 338 (1993), pp. 405-430.
8. A. FRIEDMAN AND M. VOGELIUS, Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence, Arch. Ration. Mech. Anal., 105 (1989), pp. 299-326.
9. F. HETTLICH AND W. RUNDELL, The determination of a discontinuity in a conductivity from a single boundary measurement, Inverse Problems, 14 (1998), pp. 67-82.
10. M. IKEHATA AND S. SILTANEN, Numerical method for finding the convex hull of an inclusion in conductivity from boundary measurements, Inverse Problems, 16 (2000), pp. 1043-1052.
11. H. KANG AND J. K. SEO, Identification of domains with near-extreme conductivity: Global stability and error estimates, Inverse Problems, 15 (1999), pp. 851-867.
12. H. KANG AND J. K. SEO, Recent progress in the inverse conductivity problem with single measurement, in Inverse Problems and Related Fields, CRC Press, Boca Raton, FL, 2000, pp. 69-80.
13. R. E. KLEINMAN AND T. B. A. SENIOR, Rayleigh scattering, in Low and High Frequency Asymptotics, V. K. Varadan and V. V. Varadan, eds., North-Holland, Amsterdam, 1986, pp. 1-70.
14. R. KRESS, Linear Integral Equations, Appl. Math. Sci. 82, Springer, New York, 1989.
15. O. KWON, J. K. SEO, AND J. R. YOON, A real-time algorithm for the location search of discontinuous conductivities with one measurement, Comm. Pure Appl. Math., 55 (2002), pp. 1-29.
16. A. B. MOVCHAN AND S. K. SERKOV, The Pólya-Szegö matrices in asymptotic models of dilute composite, European J. Appl. Math., 8 (1997), pp. 595-621.
17. G. PÓLYA AND G. SZEGÖ, Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Stud. 27, Princeton University Press, Princeton, NJ, 1951.
18. M. SCHIFFER AND G. SZEGÖ, Virtual mass and polarization, Trans. Amer. Math. Soc., 67 (1949), pp. 130-205.
19. C. TOMALSKY AND A. WIEGMANN, Recovery of small perturbations of an interface for an elliptic inverse problem via linearization, Inverse Problems, 15 (1999), pp. 401-411.