Hamilton system is one of the three basic forms to describe various conservative physical and mechanical processes, and it is a kind of ordinary differential equation or partial differential equation with special geometric structure. The geometric structure of the system-symplectic structure is the mathematical basis of the system. After 1980s, Academician Feng Kang, who is engaged in computational mathematics, systematically put forward the symplectic geometry algorithm of Hamiltonian system for the first time, which solved a series of theoretical and numerical calculation problems and achieved results far superior to the existing methods, and made universally recognized achievements in the field of mathematics. This pioneering work has led to the international study of multi-symplectic schemes, and has been successfully applied in celestial mechanics, molecular dynamics, rigid body and multi-rigid body motion, field theory and other fields. Thus creating a new field full of vitality and broad development prospects.