弱不连续问题高阶有限元离散系统的GAMG法

发布时间：2018-05-21 00:22

本文选题：弱不连续问题 + 高阶单元　；参考：《计算力学学报》2017年01期

【摘要】：弱不连续问题(如含夹杂问题)是固体力学计算中的一类重要问题。高阶有限元方法由于其具有更好的逼近效果,是确保数值解在界面保持较高精度的计算方法之一。但与线性元相比,高阶单元需要更多的计算机存储单元,具有更高的计算复杂性。本文利用两水平算法的思想,将高阶有限元离散系统化归于线性元离散系统的求解,为弱不连续问题高阶有限元离散系统设计了一种新的基于几何与分析信息的代数多重网格(GAMG)法,并应用于圆形求解域含单夹杂问题的高阶有限元离散系统的求解。数值试验结果表明,相比于常用GAMG法,新方法的迭代次数基本不依赖于问题规模、单元阶次以及杨氏模量的间断性,CPU计算时间得到明显改善,具有更好的计算效率和鲁棒性,可大大提高弱不连续问题有限元分析的整体效率。
[Abstract]:Weak discontinuous problem (such as inclusion problem) is an important problem in solid mechanics calculation. High order finite element method (HFEM) is one of the methods to ensure the high accuracy of numerical solution at the interface because of its better approximation effect. However, compared with linear elements, higher order cells require more computer memory cells and have higher computational complexity. In this paper, the idea of two-level algorithm is used to systematize the high-order finite element discretization to the solution of linear element discrete system. A new algebraic multigrid GAMG method based on geometric and analytical information is designed for high order finite element discrete systems with weak discontinuities. The method is applied to the solution of high order finite element discrete systems with single inclusions in circular domain. The numerical results show that the iteration number of the new method is not dependent on the size of the problem, and the computing time of the unit order and the intermittent Young's modulus is improved obviously, and the calculation efficiency and robustness of the new method are better than that of the conventional GAMG method. The overall efficiency of finite element analysis for weak discontinuous problems can be greatly improved.
【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(11601462) 湖南省自然科学基金(14JJ2063) 湖南省教育厅资助科研项目(15A183)资助项目
【分类号】：O34;O302

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