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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 4 - Gu
ido Lombardi (Politecnico di Torino\; Politecnico
di Torino)\; J.M.L. Bernard (ENS de Cachan)
DTSTART;TZID=Europe/London:20190809T103000
DTEND;TZID=Europe/London:20190809T114500
UID:TALK128305AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128305
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. Furt
hermore we think that SM and WH applied to the sam
e problems (for instance the polygon diffraction)&
nbsp\; can determine a helpful synergy. In the pas
t the SM and WH methods were considered disconnect
ed in particular because the SM method was traditi
onally defined with the angular complex representa
tion while the WH method was traditionally defined
in the Laplace domain.

In t
his course we show that the two methods have signi
ficant points of similarity when the representatio
n of problems in both methods are expressed in ter
ms of difference equations. The two methods show t
heir diversity in the solution procedures that are
completely different and effective. Both similari
ty and diversity properties are of advantage in&nb
sp\; &ldquo\;Progress and Prospects in The Theory
of Linear Waves Propagation&rdquo\;.

**Moreover both methods have demonstrated th
eir efficacy in studying particularly complex prob
lems\, beyond the traditional problem of scatterin
g by a wedge: in particular the scattering by a th
ree part polygon that we will present. Recent pr
ogress in both methods: One of the most relevant
recent progress in SM is the derivation of functio
nal difference equations without the use of Maliuz
hinets inversion theorem. **

One of t
he most relevant recent progress in WH is transfor
mation of WH equations into integral equations for
their effective solution

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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