A coupling algorithm of finite element(FE) and smoothed particle hydrodynamics(SPH) is introduced.It couples FE calculation with SPH calculation by attaching particles to element segments.In the algorithm,a particle can be fixed to an arbitrary position of an element segment and an element segment can be attached to many particles simultaneously.This makes arrangements of particles and elements at the coupling interface free.The algorithm is applied to simulate stress-wave propagation and high-velocity impact problems.It shows that the algorithm has good accuracy in simulation of stress-wave propagation.In high-velocity impact problems it achieves nearly same accuracy with higher efficiency compared with pure SPH algorithms.

Two kinds of algebraic multigrid (AMG) algorithms with three-dimensional equal algebraic structures are constructed on the basis of a two-dimensional coarsing technique.The AMG method and the corresponding algebraic multigrid-preconditioned CG method are applied to elliptic boundary value problems with smooth coefficients and anisotropic problems.Numerical results show that the AMG algorithm is efficient and robust.

A numerical method is used to study the dynamics of a model for the transport of the energy in α-helix proteins proposed by the author.The result shows that there exist static and moving localized modes in the model which may provide an alternative mechanism for the energy transport in α-helix proteins.

A model is proposed to study numerically the dynamics for the energy transportion of amide Ⅰ vibrations in proteins.The results show that there exists static and moving localized models in the mode and thus it may provides alternative mechanism of the energy transport in protein molecules.