Local refinement of flat-top partition of unity based high-order approximation

被引：2
作者：
Liu, Xiaoying [1 ,2 ]
Zhao, Zhiye [1 ]
An, Xinmei [3 ]
Jiao, Yuyong [4 ]
机构：
[1] Nanyang Technol Univ, Sch Civil & Environm Engn, Singapore 639798, Singapore
[2] Sun Yat Sen Univ, Sch Civil Engn, Guangzhou, Guangdong, Peoples R China
[3] Land Transport Author, Singapore, Singapore
[4] Chinese Acad Sci, Inst Rock & Soil Mech, Wuhan, Hubei, Peoples R China
来源：
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2018年 / 116卷 / 07期
关键词：
flat-top partition of unity; high-order approximation; linear independence; local refinement; FINITE-ELEMENT-METHOD; NUMERICAL MANIFOLD METHOD; ARBITRARY EVOLVING CRACKS; LINEAR-DEPENDENCE PROBLEM; MESHLESS METHODS; MESHFREE METHOD; PROPAGATION; SIMULATION; ENRICHMENT; FRAMEWORK;
D O I：
10.1002/nme.5932
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The high-order approximation with regularly patterned flat-top partition of unity mesh in one- and two-dimensional cases has been proven linearly independent. However, for problems with stress concentration or stress singularity, local refinement within the regular mesh is necessary to improve the accuracy and efficiency. This paper introduces local refinement of flat-top partition of unity mesh within the framework of high-order approximation in one- and two-dimensional spaces, respectively. Based on the traditional PU mesh, the construction of locally refined flat-top PU mesh is straightforward. With the rank deficiency counting approach, linear independence is proven from element level for the locally refined mesh system. Based on the numerical solution procedure presented, two numerical examples are analyzed to verify the proposed approximation method.
引用
收藏
页码：465 / 486
页数：22
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