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TZID:Europe/Paris
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UID:5149@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240514T110000
DTEND;TZID=Europe/Paris:20240514T120000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-14-2/
SUMMARY: (...): A characteristic mapping method to study kinetic equations
DESCRIPTION:: In this talk\, I will present a novel semi-Lagrangian approac
 h to solve kinetic equations numerically. I will\ndemonstrate its efficacy
  for kinetic equation by tackling the Vlasov–Poisson equation. The appro
 ach makes\nuse of the characteristic mapping method (CMM) that allows evol
 ving fine-scaled quantities on coarse\ngrids. The advected quantities are 
 constructed as the function composition of the initial condition with\nthe
  characteristic map. This flow map is a one-parameter semi-group structure
 \, which allows decomposing\nthe map into sub-maps. In contrast to other r
 efinement methods we thus use compositional refinement.\nTherefore the num
 erical solution can be in principle evaluated at any given resolution at a
 ny given time\,\npreserving the features of the initial condition like pos
 itivity.\nIn the presentation\, I will showcase the global third-order con
 vergence in both spatial and temporal\ndomains as well as the method’s e
 xceptional ability to surpass the limitations of current schemes by\nhighl
 ighting its capacity for extreme fine-scale resolution\, as depicted in fi
 g. 1. Our approach represents\na significant step forward in addressing co
 mputational challenges inherent in kinetic theories\, offering a\npathway 
 towards unprecedented precision in kinetic simulations. The talk is based 
 on the preprint [P. Krah\, X.-Y. Yin\, J. Bergmann\, J.-C. Nave\, and K. S
 chneider. A characteristic mapping method\nfor Vlasov-Poisson with extreme
  resolution properties. arXiv preprint arXiv:2311.09379\, 2023].
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20240331T030000
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