BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Numerical methods in acoustics and nonlinear dispersive partial di
 fferential equations - Georg Maierhofer (Sorbonne Universite)
DTSTART:20220307T150000Z
DTEND:20220307T160000Z
UID:TALK170852@talks.cam.ac.uk
CONTACT:Alistair Hales
DESCRIPTION:In this talk\, we will present an overview of some recent resu
 lts on numerical techniques for the solution of wave scattering problems b
 ased on the boundary integral method. To begin with\, we will study the so
 lution of these integral equations using collocation methods. We will demo
 nstrate both in practical computations and in terms of rigorous theoretica
 l results the improved convergence properties which can be achieved with t
 he use of least-squares oversampling. These collocation methods naturally 
 lead to a problem of highly oscillatory quadrature because the entries in 
 the discrete linear system representing the continuous integral equation f
 or hybrid numerical-asymptotic basis spaces are given by singular oscillat
 ory integrals. We develop efficient numerical methods that can compute the
 se integrals at frequency-independent cost. \nFinally\, based on a deep co
 nnection between oscillatory phenomena and the regularity (differentiabili
 ty) of solutions to partial differential equations on periodic domains\, w
 e will see how ideas from highly oscillatory quadrature can be used in tim
 e-stepping methods to accurately capture frequency interactions in nonline
 ar evolution equations. Based on recent advances in resonance-based integr
 ators\, this insight allows us to design innovative numerical schemes\, wh
 ich can efficiently approximate low-regularity solutions to nonlinear syst
 ems\, even when classical tools (such as Runge--Kutta methods) fail.\nThis
  is joint work with Daan Huybrechs\, Arieh Iserles\, Nigel Peake and Katha
 rina Schratz.\n
LOCATION:MR11
END:VEVENT
END:VCALENDAR