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SUMMARY:Computational Wave Propagation in the Spirit of the Geometrical Th
 eory of Diffraction - Dave Hewett (University College London)
DTSTART:20170303T094500Z
DTEND:20170303T100500Z
UID:TALK71225@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Geometrical (ray-based) techniques for high frequency wave sca
 ttering have been with us for centuries\, but until relatively recently we
 re applicable only to smooth scatterers. The Geometrical Theory of Diffrac
 tion (GTD)\, pioneered by Joe Keller and developed by numerous others sinc
 e the 1960s\, provided a powerful new methodology for scatterers with corn
 ers and sharp edges. It is a beautiful\, wide-ranging and highly intuitive
  theory\, inspired by physics but mathematically grounded in the theory of
  matched asymptotic expansions. GTD is an asymptotic theory. But it has al
 so had significant influence on the direction of research into computation
 al methods. Indeed\, the past decade has seen exciting new developments in
  `hybrid numerical-asymptotic&#39\; (HNA) methods\, which use FEM or BEM a
 pproximation spaces built from oscillatory basis functions\, which are cho
 sen by reference to the GTD. (In fact\, Keller himself published a paper d
 escribing such a method.) For many basic scattering problems HNA methods a
 chieve the `holy grail&#39\; of providing fixed accuracy with frequency-in
 dependent computational cost. In this talk I will outline the HNA approach
  and celebrate the ongoing role that Keller&#39\;s GTD is playing in its d
 evelopment.<br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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