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CATEGORIES:Lectures & Presentations
DESCRIPTION:Presenter: Beth Wingate\, Professor of Mathematics\, University
of Exeter\nDescription: Motivated by using exascale-type computer architec
tures for high resolution weather and climate simulations\, we have develop
ed phase averaging techniques for taking a large\, accurate time step with
time-parallel numerical methods in highly oscillatory PDEs. The techniques
are inspired by the method of fast singular limits that feature a mapping a
nd averaging procedure\, but for numerical methods we phase averaging over
a few oscillations using a smooth averaging kernel. We first briefly introd
uce time-parallel time stepping methods\, then discuss a proof of 'parareal
' convergence whose ingredients include bounds from fast singular limits in
the case when epsilon -> 0 and arguments developed by Gander and Hairer. S
econd\, we discuss the more general case\, when epsilon finite (and not nec
essarily small) where we show how the combination of mapping and phase aver
aging works as a coarse propagator for parareal. We give a few examples. Fi
nally\, we end with a brief outline of 3 new lines of inquiry: a proof of c
onvergence for multi-level parareal (with Juliane Rosemeier)\, alternate ma
pping that includes a mean correction to the phase averaging (with Tim Andr
ews). Finally\, we show the first explorations of this type of mapping and
averaging on the sphere (with Hiroe Yakamazi and Colin Cotter).\nBio: Beth
Wingate is a Professor of Mathematics at the University of Exeter. She did
her Ph.D. work at the University of Michigan studying numerics\, waves and
ocean fluid dynamics and spent many years at the Los Alamos National Labora
tory in New Mexico\, USA. Her research interests are mainly in geophysical
and astrophysical fluid mechanics\, mathematics\, and numerics for high-per
formance computing. Her recent research is focused on nonlinear resonance\,
Asymptotic Parallel-in-Time methods for climate modeling and High-Performa
nce Computing\, and the fluid mechanics of the slow/fast manifolds.\nHosted
by: Professor Marcella Gomez\nZoom link: https://ucsc.zoom.us/j/9997879317
7?pwd=eG9iR21RdEltUElvKzQ0TjJRUldUQT09
DTEND:20231107T010000Z
DTSTAMP:20240810T103147Z
DTSTART:20231107T000000Z
GEO:36.998035;-122.061318
LOCATION:Thimann Laboratories\, Thimann 101
SEQUENCE:0
SUMMARY:AM Seminar: On the way to the limit: phase averaging in highly osci
llatory PDEs for time-parallel numerical methods
UID:tag:localist.com\,2008:EventInstance_44694984787267
URL:https://calendar.ucsc.edu/event/am_seminar_on_the_way_to_the_limit_phas
e_averaging_in_highly_oscillatory_pdes_for_time-parallel_numerical_methods
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