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CATEGORIES:Waves Group (DAMTP)
SUMMARY:Using the Unified Transform (Fokas method) for aco
ustic scattering problems - Lorna Ayton and Matt C
olbrook
DTSTART;TZID=Europe/London:20190212T110000
DTEND;TZID=Europe/London:20190212T120000
UID:TALK119179AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/119179
DESCRIPTION:The Unified Transform maps the Helmholtz equation
to spectral space not dissimilarly to the Fourier
Transform. However\, the resulting equations from
the Unified Transform can be manipulated\, through
considering regions of analyticity\, into a so-ca
lled global relation which relates known (transfor
med) boundary conditions to unknown (transformed)
boundary data. By applying a spectral collocation
method\, the unknown boundary data can be recovere
d and the solution obtained throughout the whole d
omain. In this talk we extend previous theory for
the Unified Transform in bounded domains to unboun
ded domains so that acoustic scattering problems c
an be tackled for a range of geometries typically
approached via a matrix Wiener Hopf method. We als
o explain some of the links between the Unified Tr
ansform\, Fourier Transform and Boundary Integral
Equations. Numerical results are demonstrated for
problems with corner singularities and comparisons
made to other approaches.\n
LOCATION:CMS MR14
CONTACT:Matthew Priddin
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