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An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method

Qiao Wang, Wei Zhou, Y.T. Feng, Gang Ma, Yonggang Cheng, Xiaolin Chang, Yuntian Feng Orcid Logo

Applied Mathematics and Computation, Volume: 353, Pages: 347 - 370

Swansea University Author: Yuntian Feng Orcid Logo

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DOI (Published version): 10.1016/j.amc.2019.02.013

Abstract

The improved interpolating moving least-square (IIMLS) method has been widely used in data fitting and meshfree methods, and the obtained shape functions have the property of the delta function, compared with those obtained by the moving least-square (MLS) method. However, the moment matrix in IIMLS...

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Published in: Applied Mathematics and Computation
ISSN: 0096-3003
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa49013
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first_indexed 2019-02-28T14:06:24Z
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spelling 2019-05-13T16:20:10.9600482 v2 49013 2019-02-28 An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method d66794f9c1357969a5badf654f960275 0000-0002-6396-8698 Yuntian Feng Yuntian Feng true false 2019-02-28 CIVL The improved interpolating moving least-square (IIMLS) method has been widely used in data fitting and meshfree methods, and the obtained shape functions have the property of the delta function, compared with those obtained by the moving least-square (MLS) method. However, the moment matrix in IIMLS may be singular or ill-conditioned because of the ill quality of the point sets used. In this paper, the weighted orthogonal basis functions are applied in IIMLS to obtain a diagonal moment matrix, which can overcome the difficulty caused by directly inversing singular or ill-conditioned matrices. However, the weighted orthogonal basis functions cannot change the nature of the singular or ill-conditioned moment matrix, since the diagonal elements of the new moment matrix may be zero or close to zero. Thus, an adaptive scheme is further employed to resolve this problem by ignoring the contribution from the zero or very small diagonal elements in the diagonal moment matrix. Combined with shifted and scaled polynomial basis functions, a stabilized adaptive orthogonal IIMLS (SAO-IIMLS) approximation is obtained. Based on this approximation, a new boundary element-free method is proposed for solving elasticity problems. Numerical results for curve fitting, surface fitting and the new boundary element-free method have shown that the proposed SAO-IIMLS approximation is accurate, stable and performs well for ill quality point sets. Journal Article Applied Mathematics and Computation 353 347 370 0096-3003 Improved interpolating moving least-square, Data fitting, Boundary element-free method, Weighted orthogonal basis functions, Stabilized adaptive orthogonal IIMLS 31 12 2019 2019-12-31 10.1016/j.amc.2019.02.013 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-05-13T16:20:10.9600482 2019-02-28T09:04:49.1900719 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Qiao Wang 1 Wei Zhou 2 Y.T. Feng 3 Gang Ma 4 Yonggang Cheng 5 Xiaolin Chang 6 Yuntian Feng 0000-0002-6396-8698 7
title An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
spellingShingle An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
Yuntian Feng
title_short An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
title_full An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
title_fullStr An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
title_full_unstemmed An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
title_sort An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method
author_id_str_mv d66794f9c1357969a5badf654f960275
author_id_fullname_str_mv d66794f9c1357969a5badf654f960275_***_Yuntian Feng
author Yuntian Feng
author2 Qiao Wang
Wei Zhou
Y.T. Feng
Gang Ma
Yonggang Cheng
Xiaolin Chang
Yuntian Feng
format Journal article
container_title Applied Mathematics and Computation
container_volume 353
container_start_page 347
publishDate 2019
institution Swansea University
issn 0096-3003
doi_str_mv 10.1016/j.amc.2019.02.013
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 0
active_str 0
description The improved interpolating moving least-square (IIMLS) method has been widely used in data fitting and meshfree methods, and the obtained shape functions have the property of the delta function, compared with those obtained by the moving least-square (MLS) method. However, the moment matrix in IIMLS may be singular or ill-conditioned because of the ill quality of the point sets used. In this paper, the weighted orthogonal basis functions are applied in IIMLS to obtain a diagonal moment matrix, which can overcome the difficulty caused by directly inversing singular or ill-conditioned matrices. However, the weighted orthogonal basis functions cannot change the nature of the singular or ill-conditioned moment matrix, since the diagonal elements of the new moment matrix may be zero or close to zero. Thus, an adaptive scheme is further employed to resolve this problem by ignoring the contribution from the zero or very small diagonal elements in the diagonal moment matrix. Combined with shifted and scaled polynomial basis functions, a stabilized adaptive orthogonal IIMLS (SAO-IIMLS) approximation is obtained. Based on this approximation, a new boundary element-free method is proposed for solving elasticity problems. Numerical results for curve fitting, surface fitting and the new boundary element-free method have shown that the proposed SAO-IIMLS approximation is accurate, stable and performs well for ill quality point sets.
published_date 2019-12-31T03:59:45Z
_version_ 1763753051326251008
score 10.998116

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