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A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

Author

Listed:
  • Jufeng Wang

    (College of Finance & Information, Ningbo University of Finance & Economics, Ningbo 315175, China)

  • Fengxin Sun

    (Faculty of Science, Ningbo University of Technology, Ningbo 315016, China)

  • Rongjun Cheng

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

Abstract

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.

Suggested Citation

  • Jufeng Wang & Fengxin Sun & Rongjun Cheng, 2021. "A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions," Mathematics, MDPI, vol. 9(19), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2424-:d:646673
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    References listed on IDEAS

    as
    1. Cheng, Jing, 2021. "Analysis of commercial land leasing of the district governments of Beijing in China," Land Use Policy, Elsevier, vol. 100(C).
    2. Jing Cheng, 2020. "Data Analysis of the Factors Influencing the Industrial Land Leasing in Shanghai Based on Mathematical Models," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, April.
    3. Jufeng Wang & Fengxin Sun & Ying Xu, 2020. "Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, July.
    4. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.
    5. Cheng, Jing, 2020. "Analyzing the factors influencing the choice of the government on leasing different types of land uses: Evidence from Shanghai of China," Land Use Policy, Elsevier, vol. 90(C).
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    Cited by:

    1. Yumin Cheng, 2022. "Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”," Mathematics, MDPI, vol. 10(13), pages 1-5, June.
    2. Sun, Fengxin & Wang, Jufeng & Xu, Ying, 2024. "An improved stabilized element-free Galerkin method for solving steady Stokes flow problems," Applied Mathematics and Computation, Elsevier, vol. 463(C).

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