Reproducing Kernel Triangular B-spline-based FEM for Solving PDEs
Reproducing Kernel Triangular B-spline-based FEM for Solving PDEs
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DOI：
10.1016/j.cma.2013.08.019
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发表时间：
2013-12
影响因子：
7.2
通讯作者：
Yue Jia;Y. Zhang;Gang Xu;X. Zhuang;T. Rabczuk
中科院分区：
文献类型：
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作者：
Yue Jia;Y. Zhang;Gang Xu;X. Zhuang;T. Rabczuk
提出了一种基于再生核三角B样条的有限元方法，作为对传统三角B样条元求解偏微分方程的改进。在后者中，在整个分析域中可能发生意外的错误，主要是由于定义B样条的过度灵活性。因此，性能变得不稳定并且不能以期望的方式控制。为了解决这个问题，提出的改进，采用再生核近似的B样条核函数的计算。三种类型的偏微分方程的问题进行了测试，以验证本单元，并与传统的三角形B样条。结果表明，改进的三角B样条曲线即使在包括角点和孔洞的极端情况下也满足单位分解条件。
We propose a reproducing kernel triangular B-spline-based finite element method (FEM) as an improvement to the conventional triangular B-spline element for solving partial differential equations (PDEs). In the latter, unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the B-spline. The performance therefore becomes unstable and cannot be controlled in a desirable way. To address this issue, the proposed improvement adopts the reproducing kernel approximation in the calculation of B-spline kernel function. Three types of PDE problems are tested to validate the present element and compare against the conventional triangular B-spline. It has been shown that the improved triangular B-spline satisfies the partition of unity condition even for extreme conditions including corners and holes.