Stochastic Symplectic Methods and Numerical Ergodicity of Stochastic Nonlinear Schroinger Equation
报告人：洪佳林
报告地点：腾讯会议
报告时间：2020年08月07日星期五15:00-16:00
邀请人：李勇、冀书关
报告摘要：
In this talk we present a review on stochastic symplecticity (multi-symplecticity) and ergodicity of numerical methods for stochastic nonlinear Schroinger (NLS) equation. The equation considered is charge conservative and has the multi-symplectic conservation law. Based on a stochastic version of variational principle, we show that the phase flow of the equation, considered as an evolution equation, preserves the symplectic structure of the phase space. We give some symplectic integrators and multi-symplectic methods for the equation. By constructing control system and invariant control set, it is proved that the symplectic integrator possesses a unique invariant measure on the unit sphere. Furthermore, we obtain a full discretization which possesses the discrete charge conservation law and the discrete multi-symplectic conservation law. And the convergence error between the temporal average of the full discretization and the ergodic limit of the symplectic method is derived (In collaboration with Dr. Chuchu Chen, Dr. Xu Wang and Dr. Liying Zhang).
会议网址：https://meeting.tencent.com/s/SgPSZpvwdme2
会议ID：741 948 819
会议密码：123456
主讲人简介：
洪佳林研究员现任中国科学院数学与系统科学研究院副院长、博士导师。在随机微分方程数值方法和动力系统保结构算法研究方面做出创新性工作。在SIAM 系列期刊、J. Comput.Phys.、Math. Comput.、IMA J. Numer. Anal.、J. Differential Equations 等国际著名学术期刊上发表研究论文一百余篇。在Springer 出版社著名系列丛书Lecture Notes in Mathematics上出版专著。曾获国务院政府特殊津贴。曾主持完成国家基金委重大项目课题、国家基金委重大研究计划重点项目和集成项目等科研项目。
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