Implementation Procedures of Parallel Preconditioning with Sparse Matrix Based on FEM

Abstract

A technique to assemble global stiffness matrix stored in sparse storage format and two parallel solvers for sparse linear systems based on FEM are presented. The assembly method uses a data structure named associated node at intermediate stages to finally arrive at the Compressed Sparse Row (CSR) format. The associated nodes record the information about the connection of nodes in the mesh. The technique can reduce large memory because it only stores the nonzero elements of the global stiffness matrix. This method is simple and effective. The solvers are Restarted GMRES iterative solvers with Jacobi and sparse appropriate inverse (SPAI) preconditioning, respectively. Some numerical experiments show that the both preconditioners can improve the convergence of the iterative method, and SPAI is more powerful than Jacobi in the sence of reducing the number of iterations and parallel efficiency. Both of the two solvers can be used to solve large sparse linear system.