Proof of linear independence of flat-top PU-based high-order approximation

X.M. An; X.Y. Liu; Z.Y. Zhao; L. He

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Proof of linear independence of flat-top PU-based high-order approximation

机译：基于平顶PU的高阶逼近的线性独立性证明

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This paper extends a rank deficiency counting approach, which was initially established by An et al. (2011, 2012 [1,2]) to determine the rank deficiency of finite element partition of unity (PU)-based approximations, to explicitly prove the linear independence of the flat-top PU-based high-order polynomial approximation. The study also examines the coupled flat-top PL) and finite element PU-based approximation, and the results indicate that the space at a global level is also linearly independent for 1 -D setting and 2-D setting with triangular mesh, but not so for rectangular mesh. Moreover, a new procedure is proposed to simplify the construction of flat-top PU, and its feasibility, accuracy and efficiency have been validated by a typical numerical example.

机译：本文扩展了秩缺陷计数方法，该方法最初由An等人建立。（2011，2012 [1,2]）确定基于单位（PU）逼近的有限元划分的秩不足，以明确证明基于平顶PU的高阶多项式逼近的线性独立性。该研究还研究了基于平顶PL和有限元PU的耦合逼近，结果表明，对于具有三角形网格的一维设置和二维设置，全局水平的空间也是线性独立的，但不是所以对于矩形网格。此外，提出了一种简化平板式PU结构的新方法，并通过一个典型的数值例子验证了其可行性，准确性和效率。

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来源
《Engineering analysis with boundary elements》 |2014年第7期|104-111|共8页
作者
X.M. An; X.Y. Liu; Z.Y. Zhao; L. He;
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作者单位

School of Civil and Environnemental Engineering, Nanyang Technological University, Singapore 639798, Singapore;

School of Civil and Environnemental Engineering, Nanyang Technological University, Singapore 639798, Singapore;

School of Civil and Environnemental Engineering, Nanyang Technological University, Singapore 639798, Singapore;

School of Civil and Environnemental Engineering, Nanyang Technological University, Singapore 639798, Singapore;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Linear dependence problem; Flat-top partition of unity; Finite element partition of unity; High-order approximation;

机译：线性相关性问题;平顶分区统一;有限元划分统一;高阶近似;

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Proof of linear independence of flat-top PU-based high-order approximation

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