Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English)

Gilles Vilmart 1, 2
1 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : My research focuses on the numerical analysis of geometric and multiscale integrators for deterministic or stochastic differential equations. Numerous physical or chemical phenomena can be modeled by differential equations which possess a particular geometric or multiscale structure (e.g. Hamiltonian structures, first integrals, multiscale structures in time or in space, highly oscillatory systems), but their complexity is often so huge that a satisfactory solution is out of reach using only general purpose numerical methods. The aim is thus to identity the relevant geometric or multiscale properties of such problems, and try to take advantage of them to design and study new efficient, reliable, and accurate integrators, that reproduce the qualitative behavior of the exact solution of the considered models.
Document type :
Habilitation à diriger des recherches
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Submitted on : Tuesday, July 2, 2013 - 11:31:05 PM
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Gilles Vilmart. Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English). Analyse numérique [math.NA]. École normale supérieure de Cachan - ENS Cachan, 2013. ⟨tel-00840733⟩



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