Smart octrees: Accurately integrating discontinuous functions in 3D
Smart octrees: Accurately integrating discontinuous functions in 3D
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DOI：
10.1016/j.cma.2016.04.006
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发表时间：
2016-07
影响因子：
7.2
通讯作者：
L. Kudela;N. Zander;S. Kollmannsberger;E. Rank
中科院分区：
文献类型：
--
作者：
L. Kudela;N. Zander;S. Kollmannsberger;E. Rank
本文提出了一种高效、准确的三维背景网格上不连续函数积分方法。这个任务是很重要的计算力学应用程序中的内部接口存在于计算域。所提出的方法创建边界一致的集成子单元组成的数值求积，即使在尖锐的几何特征（如边缘或顶点）的存在下。类似于八叉树过程，该算法将切割元素细分为八个八分区。然而，八分圆节点被移动到接口上，这允许在保持算法简单性的同时对元素中的相交拓扑进行鲁棒的解析。数值算例表明，该方法能够以最少的求积点数获得高精度的区域积分。进一步的例子表明，所提出的方法提供了一个可行的替代标准八叉树为基础的方法时，结合有限单元法。
This paper presents an efficient and accurate method for the integration of discontinuous functions on a background mesh in three dimensions. This task is important in computational mechanics applications where internal interfaces are present in the computational domain. The proposed method creates boundary-conforming integration subcells for composed numerical quadrature, even in the presence of sharp geometric features (e.g. edges or vertices). Similar to the octree procedure, the algorithm subdivides the cut elements into eight octants. However, the octant nodes are moved onto the interface, which allows for a robust resolution of the intersection topology in the element while maintaining algorithmic simplicity. Numerical examples demonstrate that the method is able to deliver highly accurate domain integrals with a minimal number of quadrature points. Further examples show that the proposed method provides a viable alternative to standard octree-based approaches when combined with the Finite Cell Method.