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SUMMARY:Numerical methods for mixed boundary value problems in diffraction
  and homogenization theory - Elena Luca (University of California\, San Di
 ego)
DTSTART:20191209T163000Z
DTEND:20191209T170000Z
UID:TALK135454@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we present fast and accurate numerical methods 
 for the solution of mixed boundary value problems and of the associated ma
 trix Wiener&ndash\;Hopf problems. The Wiener&ndash\;Hopf problems are form
 ulated as Riemann&ndash\;Hilbert problems on the real line\, and the numer
 ical approach for such problems of Trogdon &amp\; Olver (2015) is employed
 . It is shown that the known far-field behaviour of the solutions can be e
 xploited to construct tailor-made numerical schemes providing accurate res
 ults. A number of scalar and matrix Wiener&ndash\;Hopf problems that gener
 alize the classical Sommerfeld problem of diffraction of plane waves by a 
 semi-infinite plane\, as well as problems arising in homogenization theory
 \, are solved using the new approach.
LOCATION:Seminar Room 1\, Newton Institute
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