三维线弹性问题有限元方程的一种并行DDM预条件子  

A Parallel DDM Preconditioner for Solving Finite Element Discretization of Elasticity Problem in Three Dimension

作　　者：冯春生[1] 舒适[1] 梁文涛 

机构地区：[1]湘潭大学数学与计算科学学院科学工程计算与数值仿真湖南省重点实验室,湖南湘潭411105

出　　处：《湘潭大学自然科学学报》2018年第1期101-106,共6页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金项目(11571293;61603322);湖南省重点研发计划(2017SK2014);湖南省自然科学基金项目(2016JJ2129);湖南省军民融合产业发展专项资金;广东省数据科学工程技术研究中心开放课题(2016KF03)

摘　　要：针对三维线弹性问题线性有限元离散系统,将非重叠区域分解法(DDM)和代数多层网格(AMG)法相结合,设计了一种基于简单粗空间的并行非重叠DDM预条件子.它本质性地将原线性代数系统的预条件子构造问题转化为三类子系统的求解问题.接着,根据三类子系统的特性分别设计相应的快速算法.最后,基于MPI+OpenMP二级并行架构,设计并实现了相应的并行PCG法.数值实验结果表明新的并行解法器具有良好的并行扩展性.In this paper,a new preconditioner is proposed for solving the linear finite element discrete system of the elastic problem in three dimension（3 D）by combining non-overlapping domain decomposition method（DDM）with algebraic multi-grid（AMG）.Firstly,a new parallel non-overlapping domain decomposition method preconditioner for the 3 Delastic problem is constructed based on a simple coarse space.It has essentially transformed the construction of this preconditioner into three subsystems to be solved.Then,the correspoding fast algorithms are proposed according to the characteristics of three subsystem respectively.Finally,the corresponding parallel PCG algorithms based on the MPI＋OpenMP two stage parallel architecture are designed and implemented.Numerical results demonstrate that the new PCG solvers possess high parallel scalability.

关 键 词：三维线弹性 非重叠区域分解法 代数多层网格法 并行扩展性 MPI+OPENMP 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O241[自动化与计算机技术—控制科学与工程]