An exponential map free implicit midpoint method for stochastic Lie-Poisson systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914157929955328 |
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| author | Ephrati, Sagy Jansson, Erik Lang, Annika Luesink, Erwin |
| author_facet | Ephrati, Sagy Jansson, Erik Lang, Annika Luesink, Erwin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An exponential map free implicit midpoint method for stochastic Lie-Poisson systems Ephrati, Sagy Jansson, Erik Lang, Annika Luesink, Erwin Numerical Analysis 60H35, 60H10, 65C30, 65P10, 37M15 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. |
| title | An exponential map free implicit midpoint method for stochastic Lie-Poisson systems |
| topic | Numerical Analysis 60H35, 60H10, 65C30, 65P10, 37M15 |
| url | https://arxiv.org/abs/2408.16701 |