Numerical computation of approximate generalized polarization tensors

References

• Astala , K and Päivärinta , L . 2006 . Calderón's inverse conductivity problem in the plane . Ann. Math. (2) , 163 : 265 – 299 .
   Web of Science ®Google Scholar
• Alessandrini , G . 1997 . Examples of instability in inverse boundary value problems . Inverse Probl. , 13 : 887 – 897 .
   Web of Science ®Google Scholar
• Ammari , H and Kang , H . 2004 . Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics , Vol. 1846 , Berlin : Springer .
   Google Scholar
• Brühl , M , Hanke , M and Vogelius , MS . 2003 . A direct impedance tomography algorithm for locating small inhomogeneities . Numer. Math. , 93 : 635 – 654 .
   Web of Science ®Google Scholar
• Capdeboscq , Y and Vogelius , MS . 2003 . A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction . M2AN Math. Model. Numer. Anal. , 37 : 159 – 173 .
   Web of Science ®Google Scholar
• Cedio-Fengya , DJ , Moskow , S and Vogelius , MS . 1998 . Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction . Inverse Probl. , 14 : 553 – 595 .
   Web of Science ®Google Scholar
• Friedman , A and Vogelius , M . 1989 . Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence . Arch. Ration. Mech. Anal. , 105 : 299 – 326 .
   Web of Science ®Google Scholar
• Ammari , H and Kang , H . 2003 . Properties of the generalized polarization tensors . Multiscale Model. Simul. , 1 : 335 – 348 . (electronic)
   Web of Science ®Google Scholar
• Ammari , H and Kang , H . 2003 . 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 : 1152 – 1166 . (electronic)
   Web of Science ®Google Scholar
• Ammari , H and Kang , H . 2007 . “ Polarization and Moment Tensors with Applications to Inverse Problems and Effective Medium Theory ” . In Applied Mathematical Sciences , Vol. 162 , New York : Springer .
   Google Scholar
• Ammari , H , Kang , H , Nakamura , G and Tanuma , K . 2002 . Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion . J. Elasticity , 67 : 97 – 129 . (2003)
   Web of Science ®Google Scholar
• Milton , GW . 2002 . The Theory of Composites , Cambridge : Cambridge Monographs on Applied and Computational Mathematics Cambridge University Press .
   Google Scholar
• Ammari , H , Kang , H and Touibi , K . 2005 . Boundary layer techniques for deriving the effective properties of composite materials . Asymptot. Anal. , 41 : 119 – 140 .
   Web of Science ®Google Scholar
• Ammari , H , Kang , H , Lim , M and Zribi , H . 2011 . The generalized polarization tensors for resolved imaging. Part I: Shape reconstruction of a conductivity inclusion . Math. Comput. , 82 : 367 – 386 .
   Google Scholar
• Ammari , H , Kang , H , Lee , H and Lim , M . 2011 . Enhancement of near cloaking using generalized polarization tensors vanishing structures. Part I: The conductivity problem , preprint available on arXiv:1104.3936v1
   Google Scholar
• Colton , D and Kress , R . 1998 . Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Applied Mathematical Sciences , Vol. 93 , Berlin : Springer-Verlag .
   Google Scholar
• Nédélec , JC . 2001 . Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems , Vol. 144 , New York : Applied Mathematical Sciences, Springer-Verlag .
   Google Scholar
• Folland , GB . 1995 . Introduction to Partial Differential Equations , 2nd , Princeton , NJ : Princeton University Press .
   Google Scholar