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Chiffres janvier 2022
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Séminaire du LJLL - 25 09 2020 14h00 : K. Schratz
Katharina Schratz (Sorbonne Université, Paris)
Resonances as a computational tool
Résumé
In recent years, a large toolbox of numerical schemes for dispersive equations has been established, based on different discretisation techniques such as discretising the variation of constants formula (e.g., exponential integrators) or splitting the full equation into a series of simpler subproblems (e.g., splitting methods). In many situations these classical schemes allow a precise and efficient approximation. This, however, drastically changes whenever non-smooth phenomena enter the scene such as for problems at low-regularity and/or with high oscillations. Classical schemes fail indeed to capture the oscillatory nature of the solution, a fact that leads to severe instabilities and loss of convergence. In this talk I present a new class of resonance based schemes. The key idea in the construction of these new schemes is to tackle and deeply embed the underlying structure of resonances into the numerical discretisation. As in the continuous case, these resonances are central to structure preservation and provide the new schemes with strong geometric properties at low regularity.
Cet exposé a eu lieu dans la salle du séminaire du Laboratoire Jacques-Louis Lions, barre 15-16, 3e étage, salle 09 (15-16-3-09) du Campus Jussieu, mais en raison de l’aggravation de la situation sanitaire à Paris, l’accès à la salle du séminaire a été limité à 15 personnes, et la retransmission simultanée à distance par Zoom a été privilégiée.