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SUMMARY:Solving Wiener-Hopf type problems numerically: a spectral method a
 pproach - Matthew Colbrook (University of Cambridge)
DTSTART:20190816T130000Z
DTEND:20190816T133000Z
UID:TALK128701@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The unified transform is typically associated with the solutio
 n of integrable nonlinear PDEs. However\, after an appropriate linearisati
 on\, one can also apply the method to linear PDEs and develop a spectral b
 oundary-based method. I will discuss recent advances of this method\, in p
 articular\, the application of the method to problems in unbounded domains
  with solutions having corner singularities. Consequently\, a wide variety
  of mixed boundary condition problems can be solved without the need for t
 he Wiener-Hopf technique. Such problems arise frequently in acoustic scatt
 ering or in the calculation of electric fields in geometries involving fin
 ite and/or multiple plates. The new approach constructs a global relation 
 that relates known boundary data\, such as the scattered normal velocity o
 n a rigid plate\, to unknown boundary values\, such as the jump in pressur
 e upstream of the plate. This can be viewed formally as a domain dependent
  Fourier transform of the boundary integral equations. By approximating th
 e unknown boundary functions in a suitable basis expansion and evaluating 
 the global relation at collocation points\, one can accurately obtain the 
 expansion coefficients of the unknown boundary values. The local choice of
  basis functions is flexible\, allowing the user to deal with singularitie
 s and complicated boundary conditions such as those occurring in elasticit
 y models or spatially variant Robin boundary conditions modelling porosity
 .
LOCATION:Seminar Room 1\, Newton Institute
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