Higher Order Global Differentiability Local Approximations for 2-D Distorted Quadrilateral Elements
Higher Order Global Differentiability Local Approximations for 2-D Distorted Quadrilateral Elements
复制标题
二维扭曲四边形单元的高阶全局可微分局部近似
DOI：
10.1080/15502280802572262
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发表时间：
2009
影响因子：
1.6
通讯作者：
J. Reddy
中科院分区：
文献类型：
--
作者：
A. Ahmadi;K. Surana;R. Maduri;A. Romkes;J. Reddy
本文发展了二维变形四边形单元的高阶整体可微局部逼近。将物理坐标空间x-y中的变形四边形单元映射成自然坐标空间中的主单元，主单元的原点位于单元的中心。对于主单元，考虑2-D C 00 p版本的分层局部近似。借用来自中间-侧节点和/或中心节点的自由度和近似函数，以导出用于在Wn空间中的各种高阶全局可微性近似的在Wn空间中的角节点处的期望导数自由度。然后，使用变换的雅可比行列式将在π η空间中的角节点处的这些导数自由度从自然坐标空间（π，η）变换到物理坐标空间（x，y），以获得xy坐标空间中的期望的高阶全局可微性局部近似。本文利用Pascal矩形建立了一个系统的方法，从C 00 p型层次元中选择自由度和相应的逼近函数，以满足xy空间中任意阶的整体可微性。已经进行了数值研究，以证明元素的性能，在精度和收敛速度方面的边界值问题所描述的自伴，非自伴和非线性微分算子，使用非失真以及失真离散化（1）。本文仅对自伴算子进行了数值研究
This paper presents development of higher order global differentiability local approximations for two dimensional quadrilateral elements of distorted geometries. The distorted quadrilateral elements in physical coordinate space x y are mapped into a master element in ξ η natural coordinate space in a two unit square with the origin at the center of the element. For the master element, 2-D C 00 p-version hierarchical local approximations are considered. The degrees of freedom and the approximation functions from the mid-side nodes and/or center node are borrowed to derive desired derivative degrees of freedom at the corner nodes in the ξ η space for various higher order global differentiability approximations in the ξ η space. These derivative degrees of freedom at the corner nodes in ξ η space are then transformed from the natural coordinate space (ξ, η) to the physical coordinate space (x, y) using Jacobians of transformations to obtain the desired higher order global differentiability local approximations in the x y coordinate space. Pascal rectangle is used to establish a systematic procedure for the selection of degrees of freedom and the corresponding approximation functions from C 00 p-version hierarchical element for the global differentiability of any desired order in x y space. Numerical studies have been conducted to demonstrate the performance of the elements in terms of accuracy and convergence rates for the boundary value problems described by self-adjoint, non-self-adjoint and non-linear differential operators using undistorted as well as distorted discretizations (1). The numerical studies in this paper are only presented for self-adjoint operator
DOI：
10.1016/b978-075063266-9/50010-x
发表时间：
2021-06
期刊：
Finite Element Analysis
影响因子：
--
作者：
G. Nikishkov
通讯作者：
G. Nikishkov
《极端条件下的XMCD研究——巡回电子系统中的磁相变——》（特邀）
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
H.;Maruyama
通讯作者：
Maruyama