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Masterclass: oscillatory Riemann-Hilbert problems

Presented by: 
Sheehan Olver
Thomas Trogdon
Friday 13th December 2019 - 09:00 to 10:00
INI Seminar Room 1
Riemann-Hilbert problems arising in applications are often oscillatory presenting challenges to their numerical solution. An effective scheme for determining their asymptotic behaviour is Deift-Zhou steepest descent, which mirrors steepest descent for oscillatory integrals by deforming to paths that turn oscillations to exponential decay. This is a fundamental 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 and non-asymptotic regime. Recent progress on going beyond steepest descent and solving oscillatory problems without deformation using GMRES is also discussed.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons