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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Wave propagation in unbounded periodic media - Son
ia Fliss (ENSTA ParisTech)
DTSTART;TZID=Europe/London:20230110T111500
DTEND;TZID=Europe/London:20230110T121500
UID:TALK193139AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/193139
DESCRIPTION:In this course I will focus on the time-harmonic w
ave equation (or Helmholtz equation) in unbounded
periodic media. One of the difficulties of the Hel
mholtz equation in an unbounded domain is that the
associated problem is not always well posed in a
classical framework. In general\, one must impose
a behavior at infinity\, called radiation conditio
n\, or derive a transparent boundary condition to
reduce the problem to a bounded domain.\nThis is a
difficult and still open question for general per
iodic media\, although the answer is now clear for
one-dimensional\, closed or open periodic wavegui
de problems. In such cases\, the framework is to u
se the limiting absorption principle. I will expla
in this approach for one-dimensional problems : &n
bsp\;(1) by adding some dissipation (i.e. an imagi
nary part of the frequency)\, one returns to a cla
ssical L2 framework (2) one can build transparent
boundary conditions based on the Dirichlet-to-Neum
ann (DtN)coefficient\, by taking advantage of the
periodic structure of the medium (3) one can study
the limit of the DtN coefficient when the dissipa
tion goes to 0.\nI will show some numerical result
s\, explain the extension to closed periodic waveg
uides and finally highlight the difficulties for m
ore general problems.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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