Rapid Solution Techniques Study In Numerical Simulation Of Injection Molding

In the numerical simulation of injection molding, FEM is used to analyze the process of flow, packing and warpage, which finally come down to the solution of sparse linear equation. And the calculation amount is very huge in the whole numerical simulation. With the element number increasing, the scale of linear equation will be bigger, and finally this will bring on the fall of calculation efficiency. Especially in the 3-D problems, this will be more prominence. Therefore, it is very valuable for theoretical and engineering application to study cost-effective algorithm and its optimization procedures to solve the equation group.Based on the sparse and symmetrical matrix of FEM equations and analyzing some current storage, this thesis chooses the chain list structure, and which makes the lowest storage requirement to computer and improves the solution efficiency. On the basis of the adequate study of general method to solve linear equation group, this thesis employs incomplete Cholesky conjugate gradient (ICCG) method for the efficiency of solution process. As this algorithm convergence is relative with the condition number of matrix. The number is bigger, the convergence is slower. So this thesis proposes an effective incomplete Cholesky decomposition preconditioned method to fall the condition number and improve the solution efficiency.The major research work in this thesis includes building up the list storage structure for global stiffness matrix from FEM, using LDL~T to get the precise solution of linear equation, using Gauss-Seidel to get the approximate solution, constructing incomplete Cholesky preconditioning matrix, using PCG to finish the fast solution of the large-scale sparse linear equation group. Numerical examples show that the combination of PCG method and list storage structure is high effective.