A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions
By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/19/2424 |
| _version_ | 1797515964444573696 |
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| author | Jufeng Wang Fengxin Sun Rongjun Cheng |
| author_facet | Jufeng Wang Fengxin Sun Rongjun Cheng |
| author_sort | Jufeng Wang |
| collection | DOAJ |
| description | By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy. |
| first_indexed | 2024-03-10T06:54:39Z |
| format | Article |
| id | doaj.art-0b1442c0f7d3439897dc3811bda000a6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T06:54:39Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0b1442c0f7d3439897dc3811bda000a62023-11-22T16:30:08ZengMDPI AGMathematics2227-73902021-09-01919242410.3390/math9192424A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight FunctionsJufeng Wang0Fengxin Sun1Rongjun Cheng2College of Finance & Information, Ningbo University of Finance & Economics, Ningbo 315175, ChinaFaculty of Science, Ningbo University of Technology, Ningbo 315016, ChinaFaculty of Maritime and Transportation, Ningbo University, Ningbo 315211, ChinaBy introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS-IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS-IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS-IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS-IMLS method. In the improved IEFG method, the DS-IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS-IMLS and the improved IEFG methods have high accuracy.https://www.mdpi.com/2227-7390/9/19/2424meshless methoddimension splitting–interpolating moving least squares (DS-IMLS) methodimproved interpolating element-free Galerkin (IEFG) methodpotential problem |
| spellingShingle | Jufeng Wang Fengxin Sun Rongjun Cheng A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions Mathematics meshless method dimension splitting–interpolating moving least squares (DS-IMLS) method improved interpolating element-free Galerkin (IEFG) method potential problem |
| title | A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions |
| title_full | A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions |
| title_fullStr | A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions |
| title_full_unstemmed | A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions |
| title_short | A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions |
| title_sort | dimension splitting interpolating moving least squares ds imls method with nonsingular weight functions |
| topic | meshless method dimension splitting–interpolating moving least squares (DS-IMLS) method improved interpolating element-free Galerkin (IEFG) method potential problem |
| url | https://www.mdpi.com/2227-7390/9/19/2424 |
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