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SUMMARY:Wave propagation in unbounded periodic media - Sonia Fliss (ENSTA 
 ParisTech)
DTSTART:20230110T111500Z
DTEND:20230110T121500Z
UID:TALK193139@talks.cam.ac.uk
DESCRIPTION:In this course I will focus on the time-harmonic wave equation
  (or Helmholtz equation) in unbounded periodic media. One of the difficult
 ies of the Helmholtz equation in an unbounded domain is that the associate
 d problem is not always well posed in a classical framework. In general\, 
 one must impose a behavior at infinity\, called radiation condition\, or d
 erive a transparent boundary condition to reduce the problem to a bounded 
 domain.\nThis is a difficult and still open question for general periodic 
 media\, although the answer is now clear for one-dimensional\, closed or o
 pen periodic waveguide problems. In such cases\, the framework is to use t
 he limiting absorption principle. I will explain this approach for one-dim
 ensional problems : &nbsp\;(1) by adding some dissipation (i.e. an imagina
 ry part of the frequency)\, one returns to a classical L2 framework (2) on
 e can build transparent boundary conditions based on the Dirichlet-to-Neum
 ann (DtN)coefficient\, by taking advantage of the periodic structure of th
 e medium (3) one can study the limit of the DtN coefficient when the dissi
 pation goes to 0.\nI will show some numerical results\, explain the extens
 ion to closed periodic waveguides and finally highlight the difficulties f
 or more general problems.
LOCATION:Seminar Room 1\, Newton Institute
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