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SUMMARY:On an analogy between the Wiener–Hopf formulations of discrete a
 nd continuous diffraction problems - Dr Andrey Korolkov\, University of Ma
 nchester
DTSTART:20250929T153000Z
DTEND:20250929T173000Z
UID:TALK235267@talks.cam.ac.uk
CONTACT:Dr Matthew Nethercote
DESCRIPTION:The talk is dedicated to unifying the framework used to derive
  the Wiener–Hopf equations arising in both discrete and continuous wave 
 diffraction problems. The main tools are the discrete Green’s identity a
 nd the appropriate notion of a discrete normal derivative. The resulting f
 ormal analogy between the Wiener–Hopf equations makes it possible to mov
 e effortlessly between the discrete and continuous formulations. The valid
 ity of this novel analogy is illustrated through several well-known two-di
 mensional canonical diffraction problems and extended to three-dimensional
  problems. Using the analogy\, embedding formulae for diffraction problems
  on square lattices are introduced and verified numerically with the metho
 d of boundary algebraic equations. Finally\, we briefly discuss the contin
 uum limit of discrete diffraction problems and indicate a way to recover t
 he continuous solution from the lattice one.
LOCATION:Centre for Mathematical Sciences MR14\, CMS
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