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SUMMARY:Coupled Parareal-Optimized Schwarz Waveform relaxation method for
advection reaction diffusion equation
DTSTART;VALUE=DATE-TIME:20180711T041500Z
DTEND;VALUE=DATE-TIME:20180711T044500Z
DTSTAMP;VALUE=DATE-TIME:20200530T054442Z
UID:indico-contribution-1747@indico.math.cnrs.fr
DESCRIPTION:Speakers: Duc Quang Bui (University Paris 13)\nParareal method
is a numerical method to solve time - evolutional problems in parallel\,
which uses two propagators: the coarse - fast and inaccurate - and the fin
e - slow but more accurate. Instead of running the fine propagator on the
whole time interval\, we divide the time space into small time intervals\,
where we can run the fine propagator in parallel to obtain the desired so
lution\, with the help of the coarse propagator and through parareal steps
. Furthermore\, each local subproblem can be solved by an iterative method
\, and instead of doing this local iterative method until convergence\, on
e may perform only a few iterations of it\, during parareal iterations. Pr
opagators then become much cheaper but sharply lose their accuracy\, and w
e hope that the convergence will be achieved across parareal iterations.
\n \nIn this talk\, we propose to couple Parareal with a well-known iter
ative method - Optimized Schwarz Waveform Relaxation (OSWR) - with only fe
w OSWR iterations in the fine propagator and with a simple coarse propagat
or deduced from Backward Euler method. We present the analysis of this cou
pled method for 1-dimensional advection reaction diffusion equation\, for
this case the convergence is almost linear. We also give some numerical il
lustrations for 1D and 2D equations\, which shows that the convergence is
much faster in practice.\n\nhttps://indico.math.cnrs.fr/event/3023/contrib
utions/1747/
LOCATION:Ho Chi Minh City University of Science
URL:https://indico.math.cnrs.fr/event/3023/contributions/1747/
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