Jean-Christophe Nave (McGill University)

Math & Stats Department Colloquium
Friday, January 17, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Jean-Christophe Nave (McGill University)

Title: Simulating problems with a wide range of scales without paying (much) for it

Abstract: In this talk I will present a new strategy to solve evolution PDEs which solutions develop a wide range of scales. Typical approaches to capture fine scales include mesh refinement (h-adaptivity) and polynomial adaptivity. I will show that by geometrizing the problem, one may leverage the semigroup structure of the solution operator. As a result, one may discretize this operator as a composition of submaps over finite time intervals. This leads to a new type of space-time adaptivity: compositional adaptivity. This approach possesses exceptional resolution properties while remaining computationally efficient. I will illustrate this technique with problems from fluid dynamics.