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SUMMARY:Using the Unified Transform (Fokas method) for acoustic scattering
  problems - Lorna Ayton and Matt Colbrook
DTSTART:20190212T110000Z
DTEND:20190212T120000Z
UID:TALK119179@talks.cam.ac.uk
CONTACT:Matthew Priddin
DESCRIPTION:The Unified Transform maps the Helmholtz equation to spectral 
 space not dissimilarly to the Fourier Transform. However\, the resulting e
 quations from the Unified Transform can be manipulated\, through consideri
 ng regions of analyticity\, into a so-called global relation which relates
  known (transformed) boundary conditions to unknown (transformed) boundary
  data. By applying a spectral collocation method\, the unknown boundary da
 ta can be recovered and the solution obtained throughout the whole domain.
  In this talk we extend previous theory for the Unified Transform in bound
 ed domains to unbounded domains so that acoustic scattering problems can b
 e tackled for a range of geometries typically approached via a matrix Wien
 er Hopf method. We also explain some of the links between the Unified Tran
 sform\, Fourier Transform and Boundary Integral Equations. Numerical resul
 ts are demonstrated for problems with corner singularities and comparisons
  made to other approaches.\n
LOCATION:CMS MR14
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