Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices
The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult. To overcome this problem, a r...
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| Published in | Applied mathematics and computation Vol. 325; pp. 120 - 145 |
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| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
15.05.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2017.12.017 |
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| Abstract | The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult. To overcome this problem, a regularized moving least-square method with nonsingular moment matrix is proposed. The shape functions obtained from the regularized MLS method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized MLS based meshless method. To overcome this problem, a regularized improved interpolating moving least-square (IIMLS) method based on the IIMLS method is also proposed. Compared with the regularized MLS method, the regularized IIMLS not only has nonsingular moment matrices, but also obtains shape functions with delta function property. Shape functions of the proposed methods are compared in 1D and 2D cases, and the methods have been applied in curve fitting, surface fitting and meshless method in numerical examples. |
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| AbstractList | The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult. To overcome this problem, a regularized moving least-square method with nonsingular moment matrix is proposed. The shape functions obtained from the regularized MLS method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized MLS based meshless method. To overcome this problem, a regularized improved interpolating moving least-square (IIMLS) method based on the IIMLS method is also proposed. Compared with the regularized MLS method, the regularized IIMLS not only has nonsingular moment matrices, but also obtains shape functions with delta function property. Shape functions of the proposed methods are compared in 1D and 2D cases, and the methods have been applied in curve fitting, surface fitting and meshless method in numerical examples. |
| Author | Cheng, Yonggang Chang, Xiaolin Miao, Yu Wang, Qiao Chen, E Ma, Gang Zhou, Wei |
| Author_xml | – sequence: 1 givenname: Qiao surname: Wang fullname: Wang, Qiao email: qiaowang@whu.edu.cn organization: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China – sequence: 2 givenname: Wei surname: Zhou fullname: Zhou, Wei email: zw_mxx@whu.edu.cn organization: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China – sequence: 3 givenname: Yonggang surname: Cheng fullname: Cheng, Yonggang organization: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China – sequence: 4 givenname: Gang orcidid: 0000-0002-1865-5721 surname: Ma fullname: Ma, Gang organization: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China – sequence: 5 givenname: Xiaolin surname: Chang fullname: Chang, Xiaolin organization: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China – sequence: 6 givenname: Yu surname: Miao fullname: Miao, Yu organization: School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China – sequence: 7 givenname: E surname: Chen fullname: Chen, E organization: Department of Civil and Environment Engineering, The Hong Kong University of Science and Technology, Kowloon, Clear Water Bay, Hong Kong |
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| Snippet | The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be... |
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| SubjectTerms | Improved interpolating moving least-square Meshless methods Moving least-square Surface construction |
| Title | Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices |
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