Advances in Computational Mathematics

, Volume 36, Issue 2, pp 235–265 | Cite as

Second-order topological expansion for electrical impedance tomography

  • M. HintermüllerEmail author
  • A. Laurain
  • A. A. Novotny


Second-order topological expansions in electrical impedance tomography problems with piecewise constant conductivities are considered. First-order expansions usually consist of local terms typically involving the state and the adjoint solutions and their gradients estimated at the point where the topological perturbation is performed. In the case of second-order topological expansions, non-local terms which have a higher computational cost appear. Interactions between several simultaneous perturbations are also considered. The study is aimed at determining the relevance of these non-local and interaction terms from a numerical point of view. A level set based shape algorithm is proposed and initialized by using topological sensitivity analysis.


Electrical impedance tomography Inverse problem Shape and topological derivative Level sets 

AMS 2000 Subject Classifications

49Q10 49K24 49N45 


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© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Department of Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  3. 3.Laboratório Nacional de Computação Científica LNCC/MCTPetropolisBrazil

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