随机多辛几何算法的构造与分析

本项目拟开展随机哈密尔顿PDEs随机多辛几何算法的构造与分析研究，主要内容包括，对随机哈密尔顿PDEs，分别结合小波插值思想与局部间断Galerkin有限元方法，研究新型随机多辛几何算法的构造；结合现代随机分析工具对所构造的随机多辛几何算法进行理论分析，包括强弱收敛性、稳定性和守恒性等。本项目的研究工作将解决随机多辛几何算法的一些重要理论问题，为数值求解随机哈密尔顿PDEs提供实用、高效的计算方法，具有重要的理论意义和应用价值。

This project will focus on the construction and analysis of stochastic multi-symplectic geometric algorithm of stochastic Hamiltonian PDEs. The main research topics include, investigating the construction of novel stochastic multi-symplectic geometric algorithm of stochastic Hamiltonian PDEs by using wavelet collocation method and local discontinuous Galerkin method, respectively; doing the theoretical analysis of stochastic multi-symplectic geometric algorithm, including strong (weak) convergence, stability and structure-preserving etc. The research works of this project will solve some important theoretical problems of stochastic multi-symplectic geometry algorithm and provide a practical and efficient method for the numerically solving of the stochastic Hamiltonian PDEs. It has the important theoretical significance and application value.