The Use of Optimization in the Reconstruction of Obstacles from Acoustic or Electromagnetic Scattering Data

  • Pierluigi Maponi
  • Maria Cristina Recchioni
  • Francesco Zirilli
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 92)


We consider some three dimensional time harmonic acoustic and electromagnetic scattering problems for bounded simply connected obstacles. We consider the following inverse problem: from the knowledge of several far field patterns generated by the obstacle when hit by known incoming waves and from the knowledge of some a-priori information about the obstacle, i.e. boundary impedance, shape symmetry, etc., reconstruct the shape or the shape and the impedance of the obstacle. There are a large number of effective numerical methods to solve the direct problem associated with this inverse problem, but techniques to solve the inverse problem are still in their infancy. We reformulate the inverse problem as two different unconstrained optimization problems. We present a review of results obtained by the authors on the inverse problem and we give some ideas concerning the solution of the direct problem by efficient parallel algorithms.


Inverse Problem Acoustic Impedance Direct Problem Scattered Field Field Pattern 
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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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Pierluigi Maponi
    • 1
  • Maria Cristina Recchioni
    • 2
  • Francesco Zirilli
    • 3
  1. 1.Dipartimento di Matematica e FisicaUniversità di CamerinoCamerinoItaly
  2. 2.Istituto di Matematica e StatisticaUniversità di AnconaAnconaItaly
  3. 3.Dipartimento di Matematica “G Castelnuovo”Università di Roma “La Sapienza”RomaItaly

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