Casimir preserving stochastic Lie-Poisson integrators

被引：1

作者：

Luesink, Erwin ^{[1
]}

Ephrati, Sagy ^{[1
]}

Cifani, Paolo ^{[1
,2
]}

Geurts, Bernard ^{[1
,3
]}

机构：

[1] Univ Twente, Fac EEMCS, Dept Appl Math, Multiscale Modelling & Simulat, POB 217, NL-7500 AE Enschede, Netherlands

[2] Gran Sasso Sci Inst, Viale F Crispi 7, I-67100 Laquila, Italy

[3] Eindhoven Univ Technol, Ctr Computat Energy Res, Dept Appl Phys, Multiscale Phys, POB 513, NL-5600 MB Eindhoven, Netherlands

来源：

ADVANCES IN CONTINUOUS AND DISCRETE MODELS | 2024年 / 2024卷 / 01期

关键词：

Stochastic Lie-Poisson integration; Hamiltonian mechanics; Stochastic differential equations; Geometric integration; Structure preservation; Lie group; Lie algebra; Coadjoint orbits; NUMERICAL-INTEGRATION; COADJOINT ORBITS; MECHANICS; EQUATIONS; TOPOLOGY;

D O I：

10.1186/s13662-023-03796-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Casimir preserving integrators for stochastic Lie-Poisson equations with Stratonovich noise are developed, extending Runge-Kutta Munthe-Kaas methods. The underlying Lie-Poisson structure is preserved along stochastic trajectories. A related stochastic differential equation on the Lie algebra is derived. The solution of this differential equation updates the evolution of the Lie-Poisson dynamics using the exponential map. The constructed numerical method conserves Casimir-invariants exactly, which is important for long time integration. This is illustrated numerically for the case of the stochastic heavy top and the stochastic sine-Euler equations.

引用

页数：23