发布时间：2019-06-14
洪佳林研究员系列学术报告
报告人简介:洪佳林，研究员、博士生导师、中国科学院数学与系统科学研究院副院长。1994年在吉林大学获得博士学位，1995年至1996年在应用数学研究所作博士后，1996年11月在计算数学与科学工程计算研究所任副研究员，1997年3月至1999年3月受西班牙科学教育部资助在西班牙Valladolid大学做研究工作，1999年1月至今，历任数学与系统科学研究院副研究员、研究员、博士生导师。其主要研究方向为动力系统保结构算法理论与应用，包括确定与随机哈密尔顿系统辛几何算法、确定与随机哈密尔顿偏微分方程多辛几何算法、李群算法以及确定与随机微分系统的守恒型算法等。主持完成国家基金委重大项目课题、重大研究计划重点项目等多个研究项目。在“J. Comput. Phys.”、“J. Diff. Equ.”、“Math. Comput.”、“Numer. Math.”、“SIAM J. Numer. Anal.”、“SIAM J. Sci. Comput.”等国际重要学术刊物上发表研究论文100余篇。
报告题一：Stochastic Symplectic Methods for Stochastic Hamiltonian Systems
报告题一摘要：In this talk we review some results on stochastic sympelctic methods for stochastic Hamiltonian systems, including stochastic generating functions, stochastic Hamilton-Jacobi theory, stochastic pseudo-symplectic methods, superiority of stochastic symplectic methods via large deviation principle and some results on numerical analysis of stochastic symplectic methods. As an important extension of stochastic symplectic methods to the infinite dimensional case, recent development of stochastic multi-symplectic methods for stochastic Hamiltonian partial differential equations will be reviewed.
报告时间: 2019年6月19日上午9:00
报告地点:科技楼南楼702室
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
报告题二：A Splitting Method for Stochastic Nonlinear
Schrödinger Equation
报告题二摘要：In this talk we present a splitting method for numerically solving stochastic nonlinear Schrödinger (NLS) equation. Based on the stability and exponential integrability of the equation, we give strong and week convergence analysis of the splitting method.
报告时间: 2019年6月19日上午10:30
报告地点:科技楼南楼702室
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
报告题三：Stochastic Symplecticity and Ergodicity of Numerical Methods
for Stochastic Nonlinear Schrödinger Equation
报告题三摘要：In this talk we present a review on stochastic symplecticity (multi-symplecticity) and ergodicity of numerical methods for stochastic nonlinear Schroedinger (NLS) equation. The equation considered is charge conservative and has the multi-symplectic conservation law. Based 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, based on the central difference scheme, possesses a unique invariant measure on the unit sphere. Furthermore, by using the midpoint scheme, we get a full discretization which possesses the discrete charge conservation law and the discrete multi-symplectic conservation law. Utilizing the Poisson equation corresponding to the finite dimensional approximation, the convergence error between the temporal average of the full discretization and the ergodic limit of the symplectic method is derived.
报告时间: 2019年6月19日下午3:00
报告地点:科技楼南楼702室
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
报告题四：Recent Development on Some Numerical Methods for Stochastic
Partial Differential Equations
报告题四摘要：In this talk we review our recent results on some important numerical issues for stochastic partial differential equations, inclusive of numerical stability, exponential integrability, invariant measure, numerical ergodicity, strong convergence and weak convergence, etc. We present stochastic symplectic methods, stochastic multi-symplecticmethods, conservative methods, splitting methods for some specific stochastic partial differential equations, such as stochastic Schroedinger equations, stochastic Maxwell equation, etc. And we study their convergence analysis, stability, exponential integrability, ergodicity and other dynamical behaviors. Convergence rates of the considered numerical methods are given. Based on Malliavin calculus, we show some results on density functions of numerical solutions for some stochastic partial differential equations. Both theoretical and numerical results are presented.
报告时间: 2019年6月19日下午4:30
报告地点:科技楼南楼702室
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~