An Adaptive Parallel Algorithm For Solving Two-dimensional Unsteady Linear Elasticity Problem

The unsteady linear elasticity model is an important mathematical model for describing elastic problems. In this work, for the two-dimensional unsteady linear elasticity model, a fully discrete scheme is given, in which the finite difference and the linear finite element method are used in the time discretization and space discretiza-tion, respectively. Numerical simulations show that the order of error is O(T+h2) in the discrete norm of L2 for the scheme mentioned above. The estimation of condi-tional for the coefficient matrix is proved, and then the corresponding adaptive fast algorithm is designed for solving the discrete scheme under the Lagrangian mesh.The influence of the mesh quality on the efficiency of the AMG-CG method is first investigated, and then an efficient AMG-CG method based on adaptive mesh opti-mization is designed. Numerical simulations show that the two adaptive algorithms are fast and robust. Finally, a parallel algorithm is designed based on the adaptive algorithm fore-mentioned, the corresponding solver modules are designed under the MPI parallel programming environment. The robustness and the extensibility of the proposed methods are investigated via numerical simulations.