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SUMMARY:Geometric numerical methods for confined Langevin dynamics - Micha
 el Tretyakov (University of Nottingham)
DTSTART:20241202T150000Z
DTEND:20241202T160000Z
UID:TALK223870@talks.cam.ac.uk
DESCRIPTION:Weak-sense numerical methods for (underdamped) Langevin dynami
 cs in bounded domains are constructed and analysed\, with both their finit
 e time convergence and convergence to ergodic limits being proved. &nbsp\;
 First-order methods are based on an Euler-type scheme interlaced with coll
 isions with the boundary. To achieve second order\,&nbsp\; composition sch
 emes are derived based on decomposition of the generator into collisional 
 drift\,&nbsp\; impulse\, and stochastic momentum evolution.&nbsp\; In a de
 terministic setting\, this approach would typically lead to first-order ap
 proximation\, even in symmetric compositions\, but we find that the stocha
 stic method can provide second-order weak approximation&nbsp\;with a singl
 e force evaluation\, both at finite times and in the ergodic limit.&nbsp\;
 &nbsp\; We provide theoretical and numerical justification for this observ
 ation using model problems and compare and contrast the numerical performa
 nce of different choices of the ordering of the terms in the splitting sch
 eme. The talk is based on a recent joint work with Ben Leimkuhler (Edinbur
 gh) and Akash Sharma (Gothenburg).
LOCATION:Seminar Room 2\, Newton Institute
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