Jiangshanshan

During doctoral studies at the Institute of Computational Mathematics, Chinese Academy of Sciences (CAS),

I focused on the theory and application of structure-preserving algorithms for Hamiltonian systems. 

My primary research topic was the construction and theoretical analysis of explicit high-precision 

multi-symplectic geometric algorithms for Hamiltonian systems. I developed computationally efficient

 and stable high-precision multi-symplectic geometric algorithms tailored for various solitary wave 

equations, accompanied by corresponding theoretical analyses. Additionally, I conducted theoretical 

assessments on the conservation quantity accuracy of multi-symplectic geometric algorithms for general

Hamiltonian systems. My research findings were published in numerous international prestigious journals,

including Numer. Math. and J. Comput. Phys. In 2007, I visited the National Institute of Informatics in 

Japan, where I delved into numerical optimization theory and advanced my understanding of further 

processing issues in numerical simulations.

During postdoctoral research at the School of Mathematics, Peking University, under the supervision 

of Professor Zhang Pingwen, I engaged in numerous practically significant tasks, primarily focusing on 

numerical simulations of fluid dynamics control equations and theoretical research on numerical 

simulations of stochastic Hamiltonian systems. I participated in several research projects funded by 

the National Natural Science Foundation of China (Grant Nos. 19971089, 10371128, 60771054), the National 

Key Basic Research Program of China (Grant No. 2005CB321700), and innovation projects from the ICMSEC 

and AMSS of CAS. I also independently undertook a China Postdoctoral Science Foundation project 

(2008-2009, Grant No. 20080430254).

Since July 2009, I have been teaching at Beijing University of Chemical Technology (BUCT), where I 

independently managed a BUCT central university research fund project (2009-2010, Grant No. QN0912), 

focusing on the application of exponentially fitted Runge-Kutta methods in Hamiltonian systems. From 

2011, I led a Youth Fund project of the National Natural Science Foundation of China (2011-2013, 

Grant No. 11001009), constructing explicit multi-symplectic geometric algorithms for multi-symplectic 

Hamiltonian systems and conducting theoretical analyses on related errors and conservation quantities. 

I analyzed the advantages of multi-symplectic geometric algorithms in long-time numerical simulations, 

conservation of physical quantities, and preservation of geometric structures. Based on the symplectic 

geometric structure of stochastic Hamiltonian systems, I proposed a theoretical framework for the 

multi-symplectic structure of stochastic Hamiltonian systems, presented significant theorems, and 

introduced novel research ideas for simulating a class of stochastic Hamiltonian systems in stochastic 

partial differential equations. Furthermore, I explored the application of stochastic differential 

equations (including backward stochastic differential equations) in economic and financial mathematics, 

particularly in areas such as option pricing. From 2015 to 2018, I participated as a collaborating 

institution in a General Program project funded by the National Natural Science Foundation of China.

My primary research area focuses on the numerical simulation of partial differential equations (PDEs), encompassing a wide range of topics including PDEs, stochastic partial differential equations (SPDEs), and numerical simulation issues related to structure-preserving systems and fluid dynamics systems. My main research approach involves high-precision methods.