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

The three-dimensional unsteady linear elastic model is widely used in many fields,such as solid mechanics,structural mechanics and fluid-solid coupling.The rapid solution of such problems is a hot research topic in science and engineering computation.In this work,for a three-dimensional unsteady linear elasticity model,In the Lagrangian grid,a fully discrete implicit schemes with the finite difference and the linear finite element method in time-space directions and the corresponding solution algorithm are given.Numerical simulations show that the finite element error function of this scheme has an error order of O??+h₂?in the discrete L₂ norm.After that,an analysis of influence of the time-space step on the condition number of the coefficients matrix of the discrete scheme is given.Furthermore,the algorithm of adaptive solution for fully discrete schemes is designed,Numerical experiments show that the method is more efficient than the commonly used CG method and AMG-CG method.Finally,a parallel algorithm based on the adaptive algorithm fore-mentioned is designed under the MPI parallel programming environment.Combined with the parallel extensibility of different solvers,an improved adaptive parallel algorithm based on spatio-temporal scale relation and corresponding solving module are designed.Numerical experiments show that the improved adaptive parallel algorithm has better efficiency.For example,the spatial split step of the initial time is 1/64,and the process number is 64,the efficiency of the new adaptive parallel algorithm is increased by 30.66%before the relative improvement.