A Parallel Ddm Preconditioner For Solving Finite Element Discretization Of Elasticity Problem In Three Dimension

Elasticity problem has wide applications in many fields, and Finite element method is one of the most commonly used methods for solving it. However, the condition number of stiffness matrix strongly depends on mesh size, which leads to great necessity to study the corresponding fast algorithms.In this paper, we first propose a new preconditioner for the linear finite element discrete system of 3D elastic problem by combining DDM and AMG. It is constructed based on simple coarse spaces and only needs to solve three classes of subsystems. Then corresponding fast algorithms are discussed respectively according to their specific characteristics. In particular, a so-called AMG-T solver is designed for the third class of subsystems by modifying the coarsening and interpolation strategies in the classical AMG(C-AMG). When the size of the subsystem is sufficiently large, experimental results show that AMG-T is better than C-AMG and CG both in the number of iteration and computing time. We also accomplish the parallel implement of the new preconditioner by using proper data structure. Numerical results show that PCG based on our new preconditioner is robust and efficient, and that it also has good scalability.