ArticleBIT. Numerical mathematics2018
Stochastic discrete Hamiltonian variational integrators.
Article in BIT. Numerical mathematics, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Accelerated Optimization on Riemannian Manifolds via Discrete Constrained Variational Integrators.Journal of nonlinear science · 2022Article
- Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations.Proceedings. Mathematical, physical, and engineering sciences · 2021Article
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Abstract
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for the stochastic flow of the Hamiltonian system. The generating function is obtained by introducing an appropriate stochastic action functional and its corresponding variational principle. Our approach permits to recast in a unified framework a number of integrators previously studied in the literature, and presents a general methodology to derive new structure-preserving numerical schemes. The resulting integrators are symplectic; they preserve integrals of motion related to Lie group symmetries; and they include stochastic symplectic Runge-Kutta methods as a special case. Several new low-stage stochastic symplectic methods of mean-square order 1.0 derived using this approach are presented and tested numerically to demonstrate their superior long-time numerical stability and energy behavior compared to nonsymplectic methods.
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