In this paper,we couple the parareal algorithm with projection methods of the trajectory on a specifc manifold,defined by the preservation of some conserved quantities of stochastic differential equations.First,projec...In this paper,we couple the parareal algorithm with projection methods of the trajectory on a specifc manifold,defined by the preservation of some conserved quantities of stochastic differential equations.First,projection methods are introduced as the coarse and fine propagators.Second,we apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm.Finally,three mumerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration,and preservation in conserved quantities of model systems.展开更多
This paper studies the geometric structure of nonlinear Schrsdinger equationand from the view-point of preserving structure a kind of fully discrete schemes ispresented for the numerical simulation of this important e...This paper studies the geometric structure of nonlinear Schrsdinger equationand from the view-point of preserving structure a kind of fully discrete schemes ispresented for the numerical simulation of this important equation in quantum. Ithas been shown by theoretical analysis and numerical experiments that such discrete schemes are quite satisfactory in keeping the desirable conservation propertiesand for simulating the long-time behaviour.展开更多
基金National Natural Science Foundation of China (Nos. 11601514,11626228 and 91630312)Beijing Natural Science Foundation (No.1152002)+1 种基金National Natural Science Foundation of China (Nos.11501570 and 11571366)National Natural Science Foundation of China (Nos.11601032,11471310 and 91630312).
文摘In this paper,we couple the parareal algorithm with projection methods of the trajectory on a specifc manifold,defined by the preservation of some conserved quantities of stochastic differential equations.First,projection methods are introduced as the coarse and fine propagators.Second,we apply the projection methods for systems with conserved quantities in the correction step of original parareal algorithm.Finally,three mumerical experiments are performed by different kinds of algorithms to show the property of convergence in iteration,and preservation in conserved quantities of model systems.
文摘This paper studies the geometric structure of nonlinear Schrsdinger equationand from the view-point of preserving structure a kind of fully discrete schemes ispresented for the numerical simulation of this important equation in quantum. Ithas been shown by theoretical analysis and numerical experiments that such discrete schemes are quite satisfactory in keeping the desirable conservation propertiesand for simulating the long-time behaviour.
