弹性力学问题自适应有限元及其局部多重网格法

刘春梅, 肖映雄, 舒适, 钟柳强

刘春梅, 肖映雄, 舒适, 钟柳强. 弹性力学问题自适应有限元及其局部多重网格法[J]. 工程力学, 2012, 29(9): 60-67,91. DOI: 10.6052/j.issn.1000-4750.2010.12.0934
引用本文: 刘春梅, 肖映雄, 舒适, 钟柳强. 弹性力学问题自适应有限元及其局部多重网格法[J]. 工程力学, 2012, 29(9): 60-67,91. DOI: 10.6052/j.issn.1000-4750.2010.12.0934
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LIU Chun-mei, XIAO Ying-xiong, SHU Shi, ZHONG Liu-qiang. ADAPTIVE FINITE ELEMENT METHOD AND LOCAL MULTIGRID METHOD FOR ELASTICITY PROBLEMS[J]. Engineering Mechanics, 2012, 29(9): 60-67,91. DOI: 10.6052/j.issn.1000-4750.2010.12.0934
Citation: LIU Chun-mei, XIAO Ying-xiong, SHU Shi, ZHONG Liu-qiang. ADAPTIVE FINITE ELEMENT METHOD AND LOCAL MULTIGRID METHOD FOR ELASTICITY PROBLEMS[J]. Engineering Mechanics, 2012, 29(9): 60-67,91. DOI: 10.6052/j.issn.1000-4750.2010.12.0934
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弹性力学问题自适应有限元及其局部多重网格法

  • 1.

    湘潭大学数学与计算科学学院,湖南,湘潭 411105;

  • 2.

    湘潭大学土木工程与力学学院,湖南,湘潭 411105;

  • 3.

    华南师范大学数学科学学院,广东,广州 510631

基金项目: 国家自然科学基金重大研究计划重点支持项目(91130002);国家自然科学基金项目(10972191);长江学者和创新团队发展计划项目(IRT1179);湖南省研究生创新基金项目(CX2010B245,CX2010B246)
详细信息
    作者简介:

    刘春梅(1981―),女,山西五台人,博士生,从事偏微分方程数值解研究(E-mail: liuchunmei8080@yahoo.com.cn);舒 适(1962―),男,湖南双峰人,教授,博士,博导,从事偏微分方程数值解及多重网格法研究(E-mail: shushi@xtu.edu.cn);钟柳强(1980―),男,广东兴宁人,博士,从事偏微分方程数值解研究(E-mail: zlq1980@gmail.com).

    通讯作者:

    肖映雄(1970―),男,湖南城步人,教授,博士,从事计算固体力学研究(E-mail: xyx610xyx@yahoo.com.cn).

  • 中图分类号: O343.3; TB115

ADAPTIVE FINITE ELEMENT METHOD AND LOCAL MULTIGRID METHOD FOR ELASTICITY PROBLEMS

  • 1.

    School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China;

  • 2.

    Civil Engineering and Mechanics College, Xiangtan University, Xiangtan, Hunan 411105, China;

  • 3.

    School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, China

More Information
    Corresponding author:

    XIAO Ying-xiong: xiao ying-xiong

摘要

    摘要
  • 摘要: 针对平面弹性力学问题,利用最新顶点二分法,设计了一种不需要标记振荡项和加密单元不需要满足“内节点”性质的自适应有限元法;利用自适应加密过程中每层网格上只有局部单元需要加密这一特性,设计了一种基于局部松弛的多重网格法.数值实验结果表明：该文设计的自适应有限元法具有一致收敛性和拟最优计算复杂度,基于局部松弛的多重网格法对求解弹性力学问题自适应网格下的有限元方程具有很好的计算效率和鲁棒性.
    Abstract: In this paper, an adaptive finite element (AFEM) method is designed by using the newest vertex bisection for linear elasticity problems in two dimensions. This method marks exclusively according to the error estimator without special treatment of oscillation and performs a minimal element refinement without the interior node property. Furthermore, a type of multigrid method based on the local relaxation is applied to the AFEM discrete systems by using the special properties during refinement. The results of various numerical experiments are shown that the proposed AFEM method is uniformly convergent and has quasi-optimal numerical complexity. The resulting multigrid method is much more robust and efficient in CPU times than the usual multigrid methods.
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    • 参考文献(18)
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出版历程
  • 收稿日期:  2010-12-16
  • 修回日期:  2011-07-20
  • 刊出日期:  2012-09-24

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