A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS
A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS
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DOI：
10.1142/s0219876208001510
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发表时间：
2008-06
影响因子：
1.7
通讯作者：
Guirong Liu
中科院分区：
文献类型：
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作者：
Guirong Liu
本文提出了一种广义梯度光滑技术，相应的光滑双线性形式，和光滑Galerkin弱形式，适用于创建一个广泛的一类有效的数值方法具有特殊的性质，包括上限性质。本文首先提出了一种广义梯度光滑技术，通过在含有不连续线段的光滑域上“粗暴地”执行绿色定理，计算含有不连续线段的位移函数的光滑应变场。利用广义梯度光滑技术和以各种方式构造的光滑域，为Galerkin公式引入了一个光滑双线性形式。基于这种光滑双线性形式发展的数值方法将是空间稳定和收敛的，并具有三个主要的重要性质：（1）它是变分相容的，如果在希尔伯特空间中寻求解决方案;（2）离散模型的刚度将减少比较...
This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced comp...