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

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

doi: 10.21656/1000-0887.380035
Funds:  The National Natural Science Foundation of China(11601462)
  • Received Date: 2017-02-16
  • Rev Recd Date: 2017-11-30
  • Publish Date: 2018-06-15
  • When the finite element method is applied to analyze the 3D thin-walled structures, some thin hexahedral elements are usually used in order to reduce the number of elements, and the corresponding higher-order elements are preferred since they have some obvious advantages in the calculation accuracy, the anti-distortion degree and so on. However, they have much higher computational complexity than the lower-order (e.g., linear) elements and the coefficient matrix of the linear algebraic equation system is severely ill-conditioned. The convergence of the commonly used solvers will deteriorate with the increasing size of the problem. An efficient and robust multi-level method was presented for the hierarchical quadratic discretizations of 3D thin-walled structures through combination of two special local block Gauss-Seidel smoothers and the DAMG algorithm based on the distance matrix. Since a hierarchical basis is used, those algebraic criteria are not needed to judge the relationships between the unknown variables and the geometric node types, and the grid transfer operators are also trivial. This makes it easy to find the coarse level (linear element) matrix derived directly from the fine level matrix, and thus the overall efficiency is greatly improved. The numerical results verify the efficiency and robustness of the proposed method.
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