Polynomial shape functions on the logarithmic space: the LogFE method
Polynomial shape functions on the logarithmic space: the LogFE method
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对数空间上的多项式形函数：LogFE 方法
DOI：
10.1002/pamm.201510225
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Wackerfuß
中科院分区：
文献类型：
--
作者：
Christian Schröppel;J. Wackerfuß
我们将[1]中提出的一种求解边值问题的新的有限元方法--对数有限元方法推广到一组完整的自由度，即三维中的平移和旋转自由度。与标准的Ritz-Galerkin公式不同，形状函数是在变形函数的对数空间上给出的。与基于李群的现有公式不同，它们可以包括任意次数的多项式函数。该方法侧重于减少误差中的低频分量，同时最大限度地减少虚假的高频变形，这一特性在多重网格算法的背景下特别有利，其中该方法可用于构建粗网格的近似。（© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA，魏因海姆）
We extend the Logarithmic finite element method, a novel finite element approach for solving boundary‐value problems proposed in [1], to a complete set of degrees of freedom, i.e. translational and rotational degrees of freedom in three dimensions. In contrast to the standard Ritz‐Galerkin formulation, the shape functions are given on the logarithmic space of the deformation function. Unlike existing formulations based on Lie groups, they may include polynomial functions of arbitrary degree. The method focuses on reducing the low‐frequency components in the error, while minimizing spurious high‐frequency deformations, a characteristic that is particularly advantageous in the context of a multigrid algorithm, in which the method may be used to construct an approximation for the coarse grid. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)