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三维薄结构热传导问题分层二次元方程的多水平方法

张申 肖映雄 郭瑞奇

张申, 肖映雄, 郭瑞奇. 三维薄结构热传导问题分层二次元方程的多水平方法[J]. 应用数学和力学, 2018, 39(6): 700-713. doi: 10.21656/1000-0887.380035
引用本文: 张申, 肖映雄, 郭瑞奇. 三维薄结构热传导问题分层二次元方程的多水平方法[J]. 应用数学和力学, 2018, 39(6): 700-713. doi: 10.21656/1000-0887.380035
ZHANG Shen, XIAO Yingxiong, GUO Ruiqi. A Multi-Level Method for Hierarchical Quadratic Discretizations of Thin-Walled Structures in 3D Heat Conduction[J]. Applied Mathematics and Mechanics, 2018, 39(6): 700-713. doi: 10.21656/1000-0887.380035
Citation: ZHANG Shen, XIAO Yingxiong, GUO Ruiqi. A Multi-Level Method for Hierarchical Quadratic Discretizations of Thin-Walled Structures in 3D Heat Conduction[J]. Applied Mathematics and Mechanics, 2018, 39(6): 700-713. doi: 10.21656/1000-0887.380035

三维薄结构热传导问题分层二次元方程的多水平方法

doi: 10.21656/1000-0887.380035
基金项目: 国家自然科学基金(11601462);湖南省教育厅资助科研项目(15A183)
详细信息
    作者简介:

    张申(1990—),男,硕士生(E-mail: zhangshenf@126.com);肖映雄(1970—),男,教授,博士(通讯作者. E-mail: xyx610xyx@xtu.edu.cn);郭瑞奇(1993—),男,硕士生(E-mail: 191522177@qq.com).

  • 中图分类号: O343.3;TB115

A Multi-Level Method for Hierarchical Quadratic Discretizations of Thin-Walled Structures in 3D Heat Conduction

Funds: The National Natural Science Foundation of China(11601462)
  • 摘要: 在利用有限元法对三维薄结构进行分析时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势.但与低阶元相比,高阶单元需要更多的计算机存储空间,离散化线性系统具有更高的计算复杂性,并且系数矩阵是严重病态的,采用通常的求解方法其效率将大大降低.该文针对三维薄结构稳态热传导问题,利用局部块Gauss-Seidel光滑子和基于“距离矩阵”的DAMG法,为其分层二次元离散系统设计了一种具有更好计算效率和鲁棒性(robustness)的多水平方法.由于采用了分层基,程序实现中不再需要建立判定未知数变量指标与所属几何节点类型对应关系的代数判据,网格转换算子的构造也变得非常简单,从而大大提高了运算效率.数值实验结果验证了该方法的有效性和鲁棒性.
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出版历程
  • 收稿日期:  2017-02-16
  • 修回日期:  2017-11-30
  • 刊出日期:  2018-06-15

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