BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The Fredholm factorization technique of Generalized Wiener-Hopf Eq
 uations in Wave scattering problems - Prof. Guido Lombardi\, Politecnico d
 i Torino\, Italy
DTSTART:20180920T100000Z
DTEND:20180920T110000Z
UID:TALK109342@talks.cam.ac.uk
CONTACT:Matthew Priddin
DESCRIPTION:Recently\, we have proposed the Generalized Wiener-Hopf Techni
 que (GWHT) that is a novel and effective spectral technique to solve scatt
 ering problems constituted of isolated impenetrable and penetrable wedges.
  The Wiener-Hopf (WH) method is a well-established technique to solve prob
 lems in all branches of engineering\, mathematical physics and applied mat
 hematics. In our opinion\, the GWHT together with the SM technique and the
  methods based on the KL transform completes the spectral techniques capab
 le to handle isolated wedge problems. \n\nRecently\, the GWHT is able to f
 urther extend the class of solvable problems\, in particular for the capab
 ility to handle complex scattering problems constituted of angular and rec
 tangular/layer shapes. \n\nThe GWHT can now easily formulate complex scatt
 ering problems in terms of Generalized Wiener-Hopf equations (GWHEs). Alth
 ough\, in general\, the relevant GWHEs of the problems cannot be solved in
  closed form\, this limit has been successfully overcome by resorting to t
 he Fredholm Factorization. The Fredholm factorization is a semi-analytical
  method that provides very accurate approximate solutions of GWHEs of a gi
 ven problem. Its efficiency is based on the reduction of the classical fac
 torization problem to system of Fredholm integral equations of second kind
 \, by eliminating some of the WH unknowns via contour integration. The ben
 efit of the semi-analytical solution is that the solution can be analyzed 
 in terms of field components via inverse spectral transformation and asymp
 totics.\n\nThe application of the GWHT consists of four steps: \n\n# Deduc
 tion of GWHEs in spectral domain possibly with the help of equivalent netw
 ork modelling\, \n# Approximate solution via Fredholm factorization\, \n# 
 Analytic continuation of the approximate solution\, \n# Evaluation of fiel
 d with physical interpretation. \n\nIn steps 1-2 network modelling orders 
 and systematizes the procedure to obtain the spectral equations for comple
 x problems avoiding redundancy. Moreover\, in practice\, steps 2 and 3 sub
 stitute the fundamental procedure of the classical WH technique\, i.e. 1) 
 the factorization of the kernel\, 2) the computation of solution via decom
 position and 3) the application of Liouville’s Theorem.\n
LOCATION:CMS\, MR12
END:VEVENT
END:VCALENDAR