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DTSTAMP:20210916T132454Z
LOCATION:Jean Calvin
DTSTART;TZID=Europe/Stockholm:20210708T180000
DTEND;TZID=Europe/Stockholm:20210708T183000
UID:submissions.pasc-conference.org_PASC21_sess165_msa354@linklings.com
SUMMARY:Time Parallel Integration and Phase Averaging for the Nonlinear Sh
allow Water Equations on the Sphere
DESCRIPTION:Minisymposium\n\nTime Parallel Integration and Phase Averaging
for the Nonlinear Shallow Water Equations on the Sphere\n\nYamazaki, Cott
er\n\nIn this talk, we present a phase averaging framework for the rotatin
g shallow water equations, discretised using compatible finite element met
hods. Phase averaging consists of averaging the nonlinearity over phase sh
ifts in the exponential of the linear wave operator. Phase averaging is a
form of heterogeneous multiscale method that aims to capture the slow dyna
mics in a solution that is smoother in time (in transformed variables) so
that larger timesteps may be taken. Following Peddle et al (2019), we cons
ider finite width phase averaging windows, since the equations have a fini
te timescale separation. In a numerical implementation, the averaging inte
gral is replaced by a Riemann sum, where each term can be evaluated in par
allel. This creates an opportunity for parallelism in the timestepping met
hod, which we use here to compute our solutions. We will describe the phas
e averaging procedure, and how it can be applied to the rotating shallow w
ater equations, together with our approach to timestepping these equations
. We will examine the impact of the averaging on the rotating shallow wate
r solution through our numerical results which confirm that there is an op
timal averaging window value for a given time step.\n\nDomain: CS and Math
, Climate and Weather
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