随机偏微分方程多辛几何算法及不确定性量化

项目名称： 随机偏微分方程多辛几何算法及不确定性量化

项目编号： No.91530118

项目类型： 重大研究计划

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 洪佳林

作者单位： 中国科学院数学与系统科学研究院

项目金额： 75万元

中文摘要： 本项目聚焦于随机偏微分方程多辛几何算法及不确定量化研究。主要研究：随机哈密尔顿偏微分方程多辛几何算法的构造和强(弱)收敛阶、稳定性等数值分析理论；量子物理和无线电统计物理中几类高维随机偏微分方程高效随机多辛几何算法；随机偏微分方程不确定量化中的自适应随机配置方法构造和数值分析；基于不确定性量化方法提高随机多辛几何算法等相关数值方法的数值计算效率。本项目的研究将完善、深化进而升华已取得关于随机偏微分方程多辛几何算法及不确定性量化的研究成果，促进随机偏微分方程数值算法的进一步创新发展。

中文关键词： 随机辛几何算法；随机多辛几何算法；随机偏微分方程；数值遍历性；不确定性量化

英文摘要： In this project, we focus on the investigation of multi-symplectic geometry algorithms and uncertainty qualification for stochastic partial differential equations. The main content of this project includes: the construction of the multi-symplectic geometry algorithms for stochastic Hamiltonian partial differential equations and the analysis of the strong (weak) order of convergence, stability, backward error analysis and so on；the study of the efficient stochastic multi-symplectic geometry algorithms for specific stochastic partial differential equations which come from quantum physics and radio statistical physics; the design and analysis of the self-adaptive stochastic collocation methods. The last but not the least is, based on the methods of uncertainty qualification, to study the numerical efficiency of stochastic multi-symplectic geometry algorithms, and to establish the connection between each other. This project will not only promote the further development of the algorithms of stochastic partial differential equations, but also boost the development of the corresponding science and technology.

英文关键词： stochastic symplectic methods；stochastic multi-symplectic methods；stochastic partial differential equations；numerical ergodicity；uncertainty quantification