计算力学学报2017，Vol.34Issue(1)：35-42,8.DOI:10.7511/jslx201701004
弱不连续问题高阶有限元离散系统的GAMG法
GAMG method for higher-order finite element discretizations of modeling weak discontinuities problems
摘要
Abstract
Weak discontinuities problems (such as inclusion problems) are important problems in solid mechanics calculation.Higher-order finite element method is a method which can ensure the accuracy of the numerical solutions near the interfaces.However,they have much higher computational complexity than the linear elements.In this paper,we present a new algebraic multigrid method (GAMG) for higher-order finite element discretizations of the weak discontinuous problems based on some geometric and analytical information by using two-level method.The resulting GAMG method is then applied to the solution of the single inclusion problem in a circular domain.Numerical results have been shown that the iteration counts of the new GAMG method do not substantially depend on the size of the problem,the number of elements and the discontinuity of Young's modulus with compared to those commonly used GAMG methods,and the CPU time is also improved obviously.Thus,the overall efficiency of the finite element analysis is greatly improved for modeling weak discontinuities problems.关键词
弱不连续问题/高阶单元/条件数/两水平方法/代数多重网格法Key words
weak discontinuities problems/higher-order elements/conditioner number/two-level method/algebraic multigrid method分类
数理科学引用本文复制引用
肖映雄,王彪,李真有..弱不连续问题高阶有限元离散系统的GAMG法[J].计算力学学报,2017,34(1):35-42,8.基金项目
国家自然科学基金(11601462) （11601462）
湖南省自然科学基金(14JJ2063) （14JJ2063）
湖南省教育厅资助科研项目(15A183)资助项目. （15A183）
