An exponential map free implicit midpoint method for stochastic Lie-Poisson systems
Preprint, 2024

An integrator for a class of stochastic Lie-Poisson systems driven by Stratonovich noise is developed. The integrator is suited for Lie-Poisson systems that also admit an isospectral formulation, which enables scalability to high-dimensional systems. Its derivation follows from discrete Lie-Poisson reduction of the symplectic midpoint scheme for stochastic Hamiltonian systems. We prove almost sure preservation of Casimir functions and coadjoint orbits under the numerical flow and provide strong and weak convergence rates of the proposed method. The scalability, structure-conservation, and convergence rates are illustrated numerically for the (generalized) rigid body, point vortex dynamics, and the two-dimensional Euler equations on the sphere.

weak convergence

stochastic Lie–Poisson system

Stratonovich noise

structure-conservation

Casimir functions

symplectic midpoint scheme

strong convergence

Författare

Sagy Ephrati

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Erik Jansson

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Annika Lang

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Erwin Luesink

Universiteit Van Amsterdam

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Ämneskategorier (SSIF 2011)

Matematik

Beräkningsmatematik

Geometri

Sannolikhetsteori och statistik

Infrastruktur

C3SE (-2020, Chalmers Centre for Computational Science and Engineering)

Chalmers e-Commons (inkl. C3SE, 2020-)

DOI

10.48550/arXiv.2408.16701

Mer information

Senast uppdaterat

2025-03-20