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SUMMARY:Masterclass: oscillatory Riemann-Hilbert problems - Sheehan Olver 
 (Imperial College London)\; Thomas Trogdon (University of Washington)
DTSTART:20191213T090000Z
DTEND:20191213T100000Z
UID:TALK135685@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Riemann-Hilbert problems arising in applications are often osc
 illatory presenting challenges to their numerical solution. An effective s
 cheme for determining their asymptotic behaviour is Deift-Zhou steepest de
 scent\, which mirrors steepest descent for oscillatory integrals by deform
 ing to paths that turn oscillations to exponential decay.  This is a funda
 mental result that lead to numerous important rigorous asymptotic results 
 over the last 35+ years. This technique proves useful for numerics as well
  providing a convergent approach that is accurate both in the asymptotic a
 nd non-asymptotic regime. Recent progress on going beyond steepest descent
  and solving oscillatory problems without deformation using GMRES is also 
 discussed.
LOCATION:Seminar Room 1\, Newton Institute
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