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CATEGORIES:Waves Group (DAMTP)
SUMMARY:The Fredholm factorization technique of Generalize
d Wiener-Hopf Equations in Wave scattering problem
s - Prof. Guido Lombardi\, Politecnico di Torino\,
Italy
DTSTART;TZID=Europe/London:20180920T110000
DTEND;TZID=Europe/London:20180920T120000
UID:TALK109342AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/109342
DESCRIPTION:Recently\, we have proposed the Generalized Wiener
-Hopf Technique (GWHT) that is a novel and effecti
ve spectral technique to solve scattering problems
constituted of isolated impenetrable and penetrab
le wedges. The Wiener-Hopf (WH) method is a well-e
stablished technique to solve problems in all bran
ches of engineering\, mathematical physics and app
lied mathematics. In our opinion\, the GWHT togeth
er with the SM technique and the methods based on
the KL transform completes the spectral techniques
capable to handle isolated wedge problems. \n\nRe
cently\, the GWHT is able to further extend the cl
ass of solvable problems\, in particular for the c
apability to handle complex scattering problems co
nstituted of angular and rectangular/layer shapes.
\n\nThe GWHT can now easily formulate complex sca
ttering problems in terms of Generalized Wiener-Ho
pf equations (GWHEs). Although\, in general\, the
relevant GWHEs of the problems cannot be solved in
closed form\, this limit has been successfully ov
ercome by resorting to the Fredholm Factorization.
The Fredholm factorization is a semi-analytical m
ethod that provides very accurate approximate solu
tions of GWHEs of a given problem. Its efficiency
is based on the reduction of the classical factori
zation problem to system of Fredholm integral equa
tions of second kind\, by eliminating some of the
WH unknowns via contour integration. The benefit o
f the semi-analytical solution is that the solutio
n can be analyzed in terms of field components via
inverse spectral transformation and asymptotics.\
n\nThe application of the GWHT consists of four st
eps: \n\n# Deduction of GWHEs in spectral domain p
ossibly with the help of equivalent network modell
ing\, \n# Approximate solution via Fredholm factor
ization\, \n# Analytic continuation of the approxi
mate solution\, \n# Evaluation of field with physi
cal interpretation. \n\nIn steps 1-2 network model
ling orders and systematizes the procedure to obta
in the spectral equations for complex problems avo
iding redundancy. Moreover\, in practice\, steps 2
and 3 substitute the fundamental procedure of the
classical WH technique\, i.e. 1) the factorizatio
n of the kernel\, 2) the computation of solution v
ia decomposition and 3) the application of Liouvil
le’s Theorem.\n
LOCATION:CMS\, MR12
CONTACT:Matthew Priddin
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