Mold-filling of polymer melt in three dimensional thin parts is a viscous incompressible flow with moving boundaries.Based on generalized Hele-Shaw flow theory,the finite element systems for pressure fields are constructed by the Control Volume Methods.The advancing of melt front is traced by a hybrid FEM/Control-Volume method and the dynamic simulation of the mold-filling process is achieved.

The relationship between ray tracing、symplectic algorithm and wave field simulation is presented. The long time conservation property of symplectic algorithm and the necessity of ray tracing using symplectic algorithm are demonstrated. In addition, wave field simulation using Maslov asymptotic theory and symplectic algorithm for linear layer model is performed. The comparison of the numerical solution with the analytic solution is carried out.

Based on Delaunay triangulation an algorithm is presented for generation triangle mesh over any planar domain which have complicated characteristic constraints.Charateritic constraints in a planar domain can be constructed by point,line,circle,arc,spline curves,open loops and closed loops which are made up of them.