Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes

被引:91
作者
An, X. M. [1 ]
Li, L. X. [2 ]
Ma, G. W. [1 ,3 ]
Zhang, H. H. [4 ]
机构
[1] Nanyang Technol Univ, Sch Civil & Environm Engn, Singapore 639798, Singapore
[2] Xi An Jiao Tong Univ, Sch Aerosp, MOE Key Lab Strength & Vibrat, Xian 710049, Shaanxi, Peoples R China
[3] Univ Western Australia, Sch Civil & Resource Engn, Crawley, WA 6009, Australia
[4] Nanchang Hangkong Univ, Sch Civil Engn & Architecture, Nanchang 330063, Jiangxi, Peoples R China
基金
中国国家自然科学基金;
关键词
Partition of unity-based methods; Linear dependence; Rank deficiency; FINITE-ELEMENT-METHOD; NUMERICAL MANIFOLD METHOD; COVER METHOD; HETEROGENEOUS SOLIDS; PERFORMANCE;
D O I
10.1016/j.cma.2010.09.013
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In the partition of unity (PU)-based methods, the global approximation is built by multiplying a partition of unity by local approximations. Within this framework, high-order approximations are achieved by directly adopting high-order polynomials as local approximations, and therefore nodes along sides or inside elements, which are usually adopted in the conventional finite element methods, are no more required. However, the PU-based approximation constructed in this way may suffer from rank deficiency due to the linear dependence of the global degrees of freedom. In this paper, the origin of the rank deficiency in the PU-based approximation space is first dissected at an element level, and then an approach to predict the rank deficiency for a mesh is proposed together with the principle of the increase of rank deficiency. Finally, examples are investigated to validate the present approach. The current work indicates such a fact that the rank deficiency is an unrelated issue to the nullity of the global matrix. It can be resolved in its own manner. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:665 / 674
页数:10
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