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BEGIN:VEVENT
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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