Free Access
Issue
ESAIM: M2AN
Volume 45, Number 6, November-December 2011
Page(s) 1193 - 1218
DOI https://doi.org/10.1051/m2an/2011015
Published online 22 July 2011
  1. R.A. Adams, Sobolev Spaces, Pure Appl. Math. 65. Academic Press, New York (1975). [Google Scholar]
  2. H. Ammari, E. Iakovleva, D. Lesselier and G. Perrusson, MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions. SIAM J. Sci. Comput. 29 (2007) 674–709. [CrossRef] [MathSciNet] [Google Scholar]
  3. 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. 34 (2003) 1152–1166. [CrossRef] [MathSciNet] [Google Scholar]
  4. H. Ammari and H. Kang, Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities. J. Math. Anal. Appl. 296 (2004) 190–208. [CrossRef] [MathSciNet] [Google Scholar]
  5. H. Ammari and H. Kang, Polarization and Moment Tensors with Applications to Inverse Problems and Effective Medium Theory, Appl. Math. Sci. 162. Springer-Verlag, Berlin (2007). [Google Scholar]
  6. H. Ammari and A. Khelifi, Electromagnetic scattering by small dielectric inhomogeneities. J. Math. Pures Appl. 82 (2003) 749–842. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Ammari, S. Moskow and M.S. Vogelius, Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM: COCV 9 (2003) 49–66. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. H. Ammari and J.K. Seo, An accurate formula for the reconstruction of conductivity inhomogeneities. Adv. Appl. Math. 30 (2003) 679–705. [CrossRef] [Google Scholar]
  9. 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. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Ammari and D. Volkov, Asymptotic formulas for perturbations in the eigenfrequencies of the full maxwell equations due to the presence of imperfections of small diameter. Asympt. Anal. 30 (2002) 331–350. [Google Scholar]
  11. H. Ammari and D. Volkov, The leading order term in the asymptotic expansion of the scattering amplitude of a collection of finite number of dielectric inhomogeneities of small diameter. Int. J. Multiscale Comput. Engrg. 3 (2005) 149–160. [CrossRef] [Google Scholar]
  12. D.N. Arnold, R.S. Falk and R. Winther, Multigrid in H(div) and H(curl). Numer. Math. 85 (2000) 197–217. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Beretta, Y. Capdeboscq, F. de Gournay and E. Francini, Thin cylindrical conductivity inclusions in a 3-dimensional domain: a polarization tensor and unique determination from boundary data. Inverse Problems 25 (2009) 065004. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Beretta and E. Francini, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities Contemp. Math. 333, edited by G. Uhlmann and G. Alessandrini, Amer. Math. Soc., Providence (2003). [Google Scholar]
  15. E. Beretta, E. Francini and M.S. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. a rigorous error analysis. J. Math. Pures Appl. 82 (2003) 1277–1301. [CrossRef] [MathSciNet] [Google Scholar]
  16. E. Beretta, A. Mukherjee and M.S. Vogelius, Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. Z. Angew. Math. Phys. 52 (2001) 543–572. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Brühl, M. Hanke and M.S. Vogelius, A direct impedance tomography algorithm for locating small inhomogeneities. Numer. Math. 93 (2003) 635–654. [CrossRef] [MathSciNet] [Google Scholar]
  18. Y. Capdeboscq and M.S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Model. Numer. Anal. 37 (2003) 159–173. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. Y. Capdeboscq and M.S. Vogelius, Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements. Math. Model. Numer. Anal. 37 (2003) 227–240. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  20. Y. Capdeboscq and M.S. Vogelius, A review of some recent work on impedance imaging for inhomogeneities of low volume fraction. Contemp. Math. 362, edited by C. Conca, R. Manasevich, G. Uhlmann and M.S. Vogelius, Amer. Math. Soc., Providence (2004). [Google Scholar]
  21. Y. Capdeboscq and M.S. Vogelius, Pointwise polarization tensor bounds, and applications to voltage perturbations caused by thin inhomogeneities. Asymptot. Anal. 50 (2006) 175–204. [MathSciNet] [Google Scholar]
  22. D. Cedio-Fengya, S. Moskow and M.S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems 14 (1998) 553–595. [CrossRef] [MathSciNet] [Google Scholar]
  23. M. Cheney, The linear sampling method and the MUSIC algorithm. Inverse Problems 17 (2001) 591–595. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. John Wiley & Sons, New York (1983). [Google Scholar]
  25. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Spectral Theory and Applications 3. Springer-Verlag, Berlin (1990). [Google Scholar]
  26. A. Friedman and M.S. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence. Arch. Rational Mech. Anal. 105 (1989) 299–326. [CrossRef] [MathSciNet] [Google Scholar]
  27. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften 224. 2nd edition, Springer-Verlag, Berlin (1998). [Google Scholar]
  28. R. Griesmaier, An asymptotic factorization method for inverse electromagnetic scattering in layered media. SIAM J. Appl. Math. 68 (2008) 1378–1403. [CrossRef] [MathSciNet] [Google Scholar]
  29. R. Griesmaier, Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Probl. Imaging 3 (2009) 389–403. [CrossRef] [MathSciNet] [Google Scholar]
  30. R. Griesmaier, Reconstruction of thin tubular inclusions in three-dimensional domains using electrical impedance tomography. SIAM J. Imaging Sci. 3 (2010) 340–362. [CrossRef] [MathSciNet] [Google Scholar]
  31. R. Griesmaier and M. Hanke, An asymptotic factorization method for inverse electromagnetic scattering in layered media II: A numerical study. Contemp. Math. 494 (2008) 61–79. [Google Scholar]
  32. R. Griesmaier and M. Hanke, MUSIC-characterization of small scatterers for normal measurement data. Inverse Problems 25 (2009) 075012. [CrossRef] [MathSciNet] [Google Scholar]
  33. E. Iakovleva, S. Gdoura, D. Lesselier and G. Perrusson, Multistatic response matrix of a 3-D inclusion in half space and MUSIC imaging. IEEE Trans. Antennas Propag. 55 (2007) 2598–2609 [CrossRef] [Google Scholar]
  34. A.M. Il'in, Matching of asymptotic expansions of solutions of boundary value problems, Translations of Mathematical Monographs 102, translated by V. Minachin, American Mathematical Society, Providence, RI (1992). [Google Scholar]
  35. A. Kirsch and N. Grinberg, The Factorization Method for Inverse Problems, Oxford Lecture Ser. Math. Appl. 36. Oxford University Press, New York (2008). [Google Scholar]
  36. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  37. P. Monk, Finite Element Methods for Maxwell's Equations. Numer. Math. Sci. Comput. Oxford University Press, New York (2003). [Google Scholar]
  38. F. Murat and L. Tartar, H-convergence, Progress in Nonlinear Differential Equations and Their Applications 31, edited by A. Cherkaev and R. Kohn. Birkhäuser, Boston (1997). [Google Scholar]
  39. W.-K. Park and D. Lesselier, MUSIC-type imaging of a thin penetrable inclusion from its multi-static response matrix. Inverse Problems 25 (2009) 075002. [CrossRef] [MathSciNet] [Google Scholar]
  40. W. Rudin, Real and complex analysis. McGraw-Hill Book Co., New York (1966). [Google Scholar]
  41. W. Rudin, Functional analysis. McGraw-Hill Series in Higher Mathematics. McGraw-Hill Book Co., New York (1973). [Google Scholar]
  42. D. Volkov, Numerical methods for locating small dielectric inhomogeneities. Wave Motion 38 (2003) 189–206. [CrossRef] [MathSciNet] [Google Scholar]
  43. C. Weber, Regularity theorems for Maxwell's equations. Math. Methods Appl. Sci. 3 (1981) 523–536. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you