PIMS-CRG Seminar / UCM Applied Math Colloquium: Seth Taylor

Lie group integrators are a class of numerical schemes for the solution of ordinary differential equations on manifolds. These methods avoid explicit representation of the solution in a coordinate chart by advancing the solution using a continuous transformation group acting on the state space. In this talk, we will present an extension of these approaches to an infinite-dimensional setting, for the numerical solution of PDEs, by replacing evolution in a truncated basis with the action of an infinite-dimensional Lie group. The resulting geometric integrators display unique properties, including analytic conservation mechanisms and subgrid-scale statistical consistency. The talk will develop the geometric ideas behind the schemes and relate them to these numerical properties through a general convergence analysis, practical implementation algorithms, and numerical experiments on a range of continuum models.