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SUMMARY:Laplace equation in a convex polygon: a numerical implementation o
 f the weak formulation of the Fokas method - Kevin Crooks\, University of 
 Cambridge
DTSTART:20130306T160000Z
DTEND:20130306T170000Z
UID:TALK42637@talks.cam.ac.uk
CONTACT:Luca Calatroni
DESCRIPTION:In this talk I will describe a numerical implementation of the
  Fokas method to solving the Laplace\nequation in a convex polygon. This f
 ollows work by Fokas (2001\, 2003) and Ashon (2012) which formulates a wea
 k variational approach in the case of a convex polygon. This method uses s
 trongly the analyticity of the Fourier Transform\, and a powerful theorem 
 by Paley and Wiener. The computational\nmethod uses a Galerkin approach wi
 th a natural sinc basis for the Paley-Wiener space. We discuss\ncomputatio
 nal issues to this approach and possible resolutions relating to its imple
 mentation. The role\nof rigorous analysis cannot be underestimated in reso
 lving these computational difficulties.
LOCATION:MR14\, Centre for Mathematical Sciences
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