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SUMMARY:From particle methods to hybrid semi-Lagrangian schemes
DTSTART;VALUE=DATE-TIME:20160616T081500Z
DTEND;VALUE=DATE-TIME:20160616T090000Z
DTSTAMP;VALUE=DATE-TIME:20191215T003445Z
UID:indico-contribution-2973@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frédérique Charles (Laboratoire Jacques-Louis Lion
s)\nParticle methods for transport equations consist in pushing forward pa
rticles along the characteristic lines of the flow\, and to describe then
the transported density as a sum of weighted and smoothed particles. Conce
ptually simple\, standard particle methods have the main drawback to produ
ce noisy solutions or to require frequent remapping.\n\nIn this talk we pr
esent two classes of particle methods which aim at improving the accuracy
of the numerical approximations with a minimal amount of smoothing.\n\nThe
idea of the Linearly Transformed Particle method is to transform the shap
e functions of particles in order to follow the local variation of the flo
w. This method has been adapted and analyzed for the Vlasov- Poisson syste
m and for a compressible aggregation equation. In both cases the error est
imate is improved compared to classical particle methods\, with the gain o
f a strong convergence of the numerical solution.\n\nHowever\, for long re
mapping periods\, shapes of particles could become to much stretched out.
The second method solve this problem of locality by combining a backward s
emi-Lagrangian approach and local linearizations of the flow. The converge
nce properties are improved and validated by numerical experiments.\nThis
is a joint work with Martin Campos-Pinto (LJLL\, UPMC).\n\nhttps://indico.
math.cnrs.fr/event/939/contributions/2973/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2973/
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