Geometric Numerical Methods for Confined Langevin Dynamics

Explore a 51-minute lecture where Professor Michael Tretyakov from the University of Nottingham delves into the construction and analysis of weak-sense numerical methods for confined Langevin dynamics in bounded domains. Learn about first-order methods based on Euler-type schemes with boundary collisions, and discover how second-order accuracy is achieved through composition schemes derived from generator decomposition into collisional drift, impulse, and stochastic momentum evolution. Understand how stochastic methods can provide second-order weak approximation with a single force evaluation, both at finite times and in the ergodic limit, despite typical limitations in deterministic settings. Examine theoretical and numerical justifications through model problems and compare different ordering approaches in splitting schemes. The lecture, part of the Stochastic Systems for Anomalous Diffusion series, presents collaborative research with Ben Leimkuhler (Edinburgh) and Akash Sharma (Gothenburg).