An efficient integration technique for the voxel‐based finite cell method
An efficient integration technique for the voxel‐based finite cell method
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DOI：
10.1002/nme.4269
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发表时间：
2012-08
影响因子：
2.9
通讯作者：
Z. Yang;M. Ruess;S. Kollmannsberger;A. Düster;E. Rank
中科院分区：
文献类型：
--
作者：
Z. Yang;M. Ruess;S. Kollmannsberger;A. Düster;E. Rank
有限元方法是一种基于高阶层次Anatz空间的虚拟区域方法。该方法避免了费时且容易出错的网格生成，并能很好地利用笛卡尔网格将复杂几何结构嵌入到简单形状的计算域中，从而将计算的部分工作量从网格生成转移到嵌入规则形状的有限单元内。本文提出了一种基于体素的线弹性模型的有效积分方法，大大减少了单元级的计算工作量。所应用的策略允许预计算单元矩阵和高阶向量的基本部分，分别表示刚度和载荷。几个基准问题表明了所提出的方法的潜力，特别是对于基于计算机断层扫描的生物医学应用中常见的不同材料属性。所应用的策略确保了时间关键型模拟的快速计算，甚至允许以高精度水平对中等大小的模型进行用户交互模拟。版权所有©2012 John Wiley&Sons，Ltd.
The finite cell method is a fictitious domain approach based on hierarchical Ansatz spaces of higher order. The method avoids time‐consuming and often error‐prone mesh‐generation and favorably exploits Cartesian grids to embed structures of complex geometry in a simple‐shaped computational domain thus shifting parts of the computational effort from mesh generation to the computation within the embedding finite cells of regular shape. This paper presents an effective integration approach for voxel‐based models of linear elasticity that drastically reduces the computational effort on cell level. The applied strategy allows the pre‐computation of an essential part of the cell matrices and vectors of higher order, representing stiffness and load, respectively. Several benchmark problems show the potential of the proposed method in particular for heterogeneous material properties as common in biomedical applications based on computer tomography scans. The applied strategy ensures a fast computation for time‐critical simulations and even allows user‐interactive simulations for models of moderate size at a high level of accuracy. Copyright © 2012 John Wiley & Sons, Ltd.