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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Highlighted lecture 1 - Iterative methods in inver
se obstacle scattering revisited - Kress\, R (Gtti
ngen)
DTSTART;TZID=Europe/London:20110726T140000
DTEND;TZID=Europe/London:20110726T150000
UID:TALK32148AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32148
DESCRIPTION:The inverse problem we consider is to determine t
he 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
concentrate on the case of scattering from a soun
d-soft obstacle or a perfect conductor. After revi
ewing some basics\, we will interpret Huygens' pri
nciple as a system of two integral equations\, nam
ed data and field equation\, for the unknown bound
ary of the scatterer and the induced surface flux.
Reflecting the ill-posedness of the inverse obsta
cle scattering problem these integral equations ar
e ill-posed. They are linear with respect to the
unknown flux and nonlinear with respect to the unk
nown boundary and offer\, in principle\, three imm
ediate possibilities for their iterative solution
via linearization and regularization.\n\nWe will d
iscuss the mathematical foundations of these algor
ithms and describe the main ideas of their numeric
al implementation. Further\, we will illuminate v
arious relations between them and exhibit connecti
ons and differences to the traditional regularize
d Newton type iterations as applied to the boundar
y to far field map. Numerical results in 3D are p
resented.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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