A Parallel Efficient Preconditioner For Solving Quadratic Finite Element Equation Of Three-dimensional Linear Elasticity Problems With Neumann Boundary Conditions

Three-dimensional linear elastic model is to describe the importance of solid mechanics and material mechanics problems model with pure Neumann boundary conditions Numerical solution of three-dimensional finite element method (FEM)is the most commonly used method of discrete lineax elastic problem, Algebraic multi-layer grid (AMG) method is a fast parallel discrete system to solve the three dimensional linear elastic problems one of the most effective method. In this paper a kind of satisfy well-posedness conditions with pure Neumann boundary conditions of three-dimensional linear elastic problems of two finite algebraic system and research its fast algorithm and parallel solver. First of all, on the basis of the article [33], we mainly study the well-posedness and fast solution of a class of linear quadratic finite element algebraic systems of three-dimensional linear elasticity problems under pure Neumann boundary condition. Then, the well-posedness of the continuous variation problem are discussed, and the well-posedness of linear quadratic finite element al-gebraic system is proved by proposing a criterion of how to remove the redundant row in stiffness matrix. Numerical experiments show that the linear quadratic fi-nite element error function in L2(?) and H1(?) norm have saturation error order.Furthermore, two kinds of solving algorithms is discussed for linear quadratic finite element algebraic system, which focuses on three combined preconditioners based on algebraic multigrid (AMG) method and Gauss Seidel iterative method (GS).With the development of corresponding conditions GMRES solver (according to the scalar and vector bsde respectively for BAG-GMRES(k )and BvAG-GMRES(k)). Nu-merical experiments verify GMRES method based on Combined preconditioner of AMG are more optimal than the commonly used method such as ILU(0) -GMRES.In comparison,the BvAG-GMRES(k) stability of the solver has better stability and solution efficiency. Finally, in the design of two kinds of serial child algorithm solver on the basis of the precondition. we design two kinds parallel algorithm of mini-mizing the data communication and the corresponding parallel solver. Numerical experiments verify the parallel algorithm has a good scalability.