Parareal Algorithms Applied to Stochastic Differential Equations with Conserved Quantities (Journal of Computational Mathematics, 2018)
In this paper, we couple the parareal algorithm with projection methods of the trajectoryon a specific manifold, defined by the preservation of some conserved quantities ofstochastic differential equations. First, projection methods are introduced as the coarseand fine propagators. Second, we apply the projection methods for systems with conservedquantities in the correction step of original parareal algorithm. Finally, three numericalexperiments are performed by different kinds of algorithms to show the property of convergencein iteration, and preservation in conserved quantities of model systems.