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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The link between the Wiener-Hopf and the generalis
ed Sommerfeld Malyuzhinets methods: Lecture 3 - Gu
ido Lombardi (Politecnico di Torino\; Politecnico
di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART;TZID=Europe/London:20190808T141500
DTEND;TZID=Europe/London:20190808T153000
UID:TALK128092AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128092
DESCRIPTION:The Sommerfeld Malyuzhinets (SM) metho
d and the Wiener Hopf (WH) technique are different
but closely related methods. In particular in the
paper &ldquo\;Progress and Prospects in The Theor
y of Linear Waves Propagation&rdquo\; SIAM SIREV v
ol.21\, No.2\, April 1979\, pp. 229-245\, J.B. Kel
ler posed the following question &ldquo\;What feat
ures of the methods account for this difference?&r
dquo\;. \; Furthermore \; J.B. Keller notes &ldquo\;it
might be helpful to understand this in order to p
redict the success of other methods&rdquo\;.
We agree with this opinion
expressed by the giant of \; Diffraction. Fur
thermore we think that SM and WH applied to the sa
me problems (for instance the polygon diffraction)
 \; can determine a helpful synergy. In the pa
st the SM and WH methods were considered disconnec
ted in particular because the SM method was tradit
ionally defined with the angular complex represent
ation while the WH method was traditionally define
d in the Laplace domain.
In
this course we show that the two methods have sign
ificant points of similarity when the representati
on of problems in both methods are expressed in te
rms of difference equations. The two methods show
their diversity in the solution procedures that ar
e completely different and effective. Both similar
ity and diversity properties are of advantage in&n
bsp\; &ldquo\;Progress and Prospects in The Theory
of Linear Waves Propagation&rdquo\;.
<
br>Moreover both methods have demonstrated t
heir efficacy in studying particularly complex pro
blems\, beyond the traditional problem of scatteri
ng by a wedge: in particular the scattering by a t
hree part polygon that we will present. Recent p
rogress in both methods: One of the most relevant
recent progress in SM is the derivation of functi
onal difference equations without the use of Maliu
zhinets inversion theorem.
One of
the most relevant recent progress in WH is transfo
rmation of WH equations into integral equations fo
r their effective solution.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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