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Layer Potential Techniques

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2098)

Abstract

The inclusion detection, localization, and reconstruction algorithms described in this book rely on asymptotic expansions of the fields when the medium contains inclusions of small volume. Such asymptotics will be investigated in the cases of the conductivity and the Helmholtz equations. As it will be shown in the subsequent chapters, a remarkable feature of these imaging techniques is that they allow a stable and accurate reconstruction of the location and of the geometric features of the inclusions, even for moderately noisy data. The amount of reconstructed information is a function of the signal-to-noise ratio in the data.

Keywords

  • Fundamental Solution
  • Neumann Problem
  • Helmholtz Equation
  • Transmission Problem
  • Dirichlet Eigenvalue

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2013 Springer International Publishing Switzerland

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Ammari, H. et al. (2013). Layer Potential Techniques. In: Mathematical and Statistical Methods for Multistatic Imaging. Lecture Notes in Mathematics, vol 2098. Springer, Cham. https://doi.org/10.1007/978-3-319-02585-8_2

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