Feng Kang - Academic Life

Academic Life

Feng Kang's scientific contributions range across many fields. Before 1957 he mainly worked on pure mathematics, specially on topological groups, Lie groups and generalized function theory. From 1957 he changed to applied mathematics and computational mathematics. Because of his sound and broad knowledge in mathematics and physics, he made a series of pioneer researches in computational mathematics.

In the later 1950s and early 1960s, based on the computations of dam constructions, Professor Feng proposed a systematic numerical method for solving partial differential equations. The method was called Finite difference method based on variation principle (基于变分原理的差分方法). This method was also independently invented in the West, called there the finite element method. It is now considered that the invention of the finite element method is a milestone of computational mathematics. In the 1970s Professor Feng gave embedding theories in the discontinuous finite element space, and generalized classical theory on elliptic equations to various dimensional combinations, which provided a mathematical foundation for elastic composite structures.

Also in the 1970s, he made great efforts and contributions in reducing elliptic equation to boundary integral equation. He gave natural boundary element method, which is now regarded as one of three main boundary element methods. From 1978 he had given lectures and seminars on finite elements and natural boundary elements in more than ten universities and institutes in France, Italy, Japan and USA.

From 1984 Professor Feng changed his research field from elliptic equations to dynamical systems such as Hamiltonian systems and wave equations. He proposed symplectic algorithms for Hamiltonian systems based on symplectic geometry. Such algorithms can preserve the symplectic geometric structure of Hamiltonian systems.

He then led and supervised a research group on the symplectic algorithms for Hamiltonian systems with finite and infinite dimensions, and on dynamical systems with Lie algebraic structures, such as contact systems, source-free systems, etc., making use of the corresponding geometry and the underlying Lie algebras and Lie groups. These algorithms are overwhelmingly superior to conventional algorithms in long term tracking and qualitative simulation in many practical applications, such as celestial mechanics, molecular dynamics, etc.