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SUMMARY:Highlighted lecture 1 - Iterative methods in inverse obstacle scat
 tering revisited - Kress\, R (Gttingen)
DTSTART:20110726T130000Z
DTEND:20110726T140000Z
UID:TALK32148@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The inverse problem we consider  is to determine the shape of 
 an obstacle from the knowledge of the far field pattern for scattering of 
 time-harmonic plane waves.  For the sake of simplicity\, we will concentra
 te on the case of scattering from a sound-soft obstacle or a perfect condu
 ctor. After reviewing some basics\, we will interpret Huygens' principle a
 s a system of two integral equations\, named data and field equation\, for
  the unknown boundary of the scatterer and the induced surface flux. Refle
 cting the ill-posedness of the inverse obstacle scattering problem these i
 ntegral equations are ill-posed.  They are linear with respect to the unkn
 own flux and nonlinear with respect to the unknown boundary and offer\, in
  principle\, three immediate possibilities for their iterative solution vi
 a linearization and regularization.\n\nWe will discuss the mathematical fo
 undations of these algorithms and describe the main ideas of their numeric
 al implementation.  Further\, we will illuminate various relations between
  them and exhibit connections  and differences to the traditional regulari
 zed Newton type iterations as applied to the boundary to far field map.  N
 umerical results in 3D are presented.\n
LOCATION:Seminar Room 1\, Newton Institute
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