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

被引：12

作者：

An, X. M. ^{[1
]}

Liu, X. Y. ^{[1
]}

Zhao, Z. Y. ^{[1
]}

He, L. ^{[1
]}

机构：

[1] Nanyang Technol Univ, Sch Civil & Environm Engn, Singapore 639798, Singapore

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2014年 / 44卷

关键词：

Linear dependence problem; Flat-top partition of unity; Finite element partition of unity; High-order approximation; FINITE-ELEMENT-METHOD; UNITY METHOD; PARTICLE-PARTITION; DEPENDENCE PROBLEM; PERFORMANCE;

D O I：

10.1016/j.enganabound.2014.04.003

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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 PU 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. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：104 / 111

页数：8

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