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SUMMARY:Discrete Helmholtz equation and the interaction of two perpendicul
 ar semi-infinite boundaries: one equation with tree unknown functions. - A
 nastasia Kisil (University of Manchester)
DTSTART:20230206T153000Z
DTEND:20230206T161500Z
UID:TALK194740@talks.cam.ac.uk
DESCRIPTION:In this talk we are interested in solving the discrete Helmhol
 tz equation on a square lattice with two perpendicular semi-infinite bound
 ary conditions. The interaction of the two boundary forms an interesting m
 ultiple scattering problem which leads to a new equation to solve. This is
  a generalisation of the classical Wiener--Hopf equation\, now in two vari
 ables and with three unknown function. A solution method for this type of 
 equation will be presented by defining an underlining manifold that links 
 the two variables. &nbsp\;Next the analyticity regions of unknown function
 s is extended and that allows to simplify the problem. As the result the p
 roblem is fully solvable in terms of Cauchy type integrals which is surpri
 sing since this is not always possible for such complicated type of proble
 ms. Some toy examples are presented to illustrate the method.
LOCATION:Seminar Room 1\, Newton Institute
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