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SUMMARY:The link between the Wiener-Hopf and the generalised Sommerfeld Ma
 lyuzhinets methods: Lecture 3 - Guido Lombardi (Politecnico di Torino\; Po
 litecnico di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART:20190808T131500Z
DTEND:20190808T143000Z
UID:TALK128092@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span><span>The Sommerfeld Malyuzhinets (SM) method and the Wi
 ener Hopf (WH) technique are different but closely related methods. In par
 ticular in the paper &ldquo\;Progress and Prospects in The Theory of Linea
 r Waves Propagation&rdquo\; SIAM SIREV vol.21\, No.2\, April 1979\, pp. 22
 9-245\, J.B. Keller posed the following question &ldquo\;What features of 
 the methods account for this difference?&rdquo\;.&nbsp\; Furthermore&nbsp\
 ; <a target="_blank" rel="nofollow">J.B. Keller</a> notes &ldquo\;it might
  be helpful to understand this in order to predict the success of other me
 thods&rdquo\;.</span>  <br></span><br><span>We agree with this opinion exp
 ressed by the giant of&nbsp\; Diffraction. Furthermore we think that SM an
 d WH applied to the same problems (for instance the polygon diffraction)&n
 bsp\; can determine a helpful synergy. In the past the SM and WH methods w
 ere considered disconnected in particular because the SM method was tradit
 ionally defined with the angular complex representation while the WH metho
 d was traditionally defined in the Laplace domain.  <br></span><br><span>I
 n this course we show that the two methods have significant points of simi
 larity when the representation of problems in both methods are expressed i
 n terms of difference equations. The two methods show their diversity in t
 he solution procedures that are completely different and effective. Both s
 imilarity and diversity properties are of advantage in&nbsp\; &ldquo\;Prog
 ress and Prospects in The Theory of Linear Waves Propagation&rdquo\;. <br>
 </span><br><span>Moreover both methods have demonstrated their efficacy in
  studying particularly complex problems\, beyond the traditional problem o
 f scattering by a wedge: in particular the scattering by a three part poly
 gon that we will present.   Recent progress in both methods:  One of the m
 ost relevant recent progress in SM is the derivation of functional differe
 nce equations without the use of Maliuzhinets inversion theorem. <br></spa
 n><br> One of the most relevant recent progress in WH is transformation of
  WH equations into integral equations for their effective solution.  <br><
 br><br>
LOCATION:Seminar Room 1\, Newton Institute
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