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Topological Derivatives for Shape Reconstruction

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Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1943)

Topological derivative methods are used to solve constrained optimization reformulations of inverse scattering problems. The constraints take the form of Helmholtz or elasticity problems with different boundary conditions at the interface between the surrounding medium and the scatterers. Formulae for the topological derivatives are found by first computing shape derivatives and then performing suitable asymptotic expansions in domains with vanishing holes. We discuss integral methods for the numerical approximation of the scatterers using topological derivatives and implement a fast iterative procedure to improve the description of their number, size, location and shape.

Keywords

  • Inverse Problem
  • Incident Wave
  • Neumann Problem
  • Boundary Integral Equation
  • Helmholtz Equation

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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Carpio, A., Rapún, M.L. (2008). Topological Derivatives for Shape Reconstruction. In: Bonilla, L.L. (eds) Inverse Problems and Imaging. Lecture Notes in Mathematics, vol 1943. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78547-7_5

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