摘要
针对一种含跳系数椭圆问题的二阶混合有限体元格式,讨论求解相应离散系统PGMRES法的预条件子构造问题.通过严格的理论分析,建立分层基下该二阶混合有限体元刚度矩阵和二次有限元刚度矩阵的谱等价关系,并利用关于二次有限元刚度矩阵的一种基于分层思想的GAMG预条件子,为二阶混合有限体元刚度矩阵设计一种高效GAMG预条件子.数值结果验证理论分析的正确性和新预条件子的高效性与稳定性.
Preconditioners for GMRES method are discussed in solving linear systems discretized from scalar elliptic partial differential equations of second order with jump coeffcient.Based on hierarchical basis,spectral equivalence is established for two kinds of stiffness matrices from quadratic finite element and second order mixed-type finite volume element method,respectively.A preconditioner is proposed by combining equivalence with two-level geometric-algebraic multigrid（GAMG） method which was especially designed for linear systems arising from quadratic finite element discretization.Numerical results confirm correctness of our theoretical analysis.It shows that the preconditioner is quite effcient and robust.
出处
《计算物理》
CSCD
北大核心
2011年第4期493-500,共8页
Chinese Journal of Computational Physics
基金
国家自然科学基金重点(11031006)
湖南省研究生创新基金(CX2010B246
CX2010B245)
国家863高技术惯性约束聚变专题
湖南省自然科学基金(10972191)资助项目
关键词
预条件子
AMG法
有限体元法
有限元法
preconditioner
AMG method
finite volume element method
finite element method
