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Local refinement of flat‐top partition of unity based high‐order approximation
Author(s) -
Liu Xiaoying,
Zhao Zhiye,
An Xinmei,
Jiao Yuyong
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5932
Subject(s) - partition of unity , partition (number theory) , mathematics , singularity , numerical analysis , independence (probability theory) , finite element method , mathematical optimization , mathematical analysis , combinatorics , structural engineering , statistics , engineering
Summary 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.