三维薄结构热传导问题Wilson元离散系统的DAMG法

发布时间：2018-05-29 18:30

本文选题：热传导问题 + 薄结构　；参考：《广西大学学报(自然科学版)》2017年04期

【摘要】：对三维薄结构问题,在进行网格剖分时,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,但也大大增加了计算复杂性。Wilson元通过在单元内部设置附加自由度的方式来提高完全多项式的次数,具有计算精度高且自由度又少的优点,因而在实际计算中被广泛使用。但要提高这种非协调元分析效率还需为相应离散系统设计好的求解方法。本文针对一般变系数三维薄结构热传导问题,建立了Wilson元计算格式,并将DAMG法应用于与8节点三线性元谱等价的Wilson元离散系统的求解。数值实验结果表明,与常用方法相比,基于"距离矩阵"的代数多重网格(DAMG)法具有更好的计算效率和鲁棒性(robustness)。
[Abstract]:In order to reduce the number of elements, the hexahedron thin element is often used in the problem of three-dimensional thin structure. The corresponding high-order element has obvious advantages in calculation accuracy, anti-distortion degree and so on. However, the computational complexity is also greatly increased. Wilson element is widely used in practical calculation because of its high accuracy and low degree of freedom, because it can increase the degree of complete polynomial by setting additional degrees of freedom inside the element. However, in order to improve the efficiency of the nonconforming element analysis, it is necessary to design a solution method for the corresponding discrete system. In this paper, for the heat conduction problem of three dimensional thin structures with variable coefficients, the Wilson element calculation scheme is established, and the DAMG method is applied to the solution of the Wilson element discrete system which is equivalent to the 8-node trilinear element spectrum. The numerical results show that the algebraic multigrid method based on distance matrix has better computational efficiency and robustness than the usual methods.
【作者单位】：湘潭大学土木工程与力学学院;
【基金】：国家自然科学基金资助项目(11601462) 湖南省教育厅资助科研项目(15A183)
【分类号】：O551.3

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