Parareal algorithms applied to stochastic differential equations with conserved quantities
For researchers in numerical simulation of stochastic differential equations, this work offers an incremental extension of existing parareal methods to handle conserved quantities.
The paper applies parareal algorithms to stochastic differential equations with conserved quantities, using projection methods to preserve invariants. Numerical experiments demonstrate convergence and conservation properties.
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are introduced as the coarse and fine propagators. Second, we also apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm. Finally, three numerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration, and preservation in conserved quantities of model systems.