IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v493y2025ics0096300324007136.html
   My bibliography  Save this article

Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently

Author

Listed:
  • Hosseinzadeh, Hossein
  • Sedaghatjoo, Zeinab

Abstract

Conventionally, piecewise polynomials have been used in the boundary element method (BEM) to approximate unknown boundary values. However, since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for high dimensional domains, this paper proposes approximating the unknown values using RBFs. This new formulation is called the radial BEM. To calculate the singular boundary integrals in the radial BEM, the authors propose a new distribution of boundary source points that removes the singularity from the integrals. This allows the boundary integrals to be precisely calculated using the standard Gaussian quadrature rule with 16 quadrature nodes. Several numerical examples are presented to evaluate the efficiency of the radial BEM compared to standard BEM and RBF collocation method for solving partial differential equations (PDEs). The analytical and numerical studies demonstrate that the radial BEM is a superior version of BEM that will significantly enhance the application of BEM and RBFs in solving PDEs.

Suggested Citation

  • Hosseinzadeh, Hossein & Sedaghatjoo, Zeinab, 2025. "Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently," Applied Mathematics and Computation, Elsevier, vol. 493(C).
    • Handle: RePEc:eee:apmaco:v:493:y:2025:i:c:s0096300324007136
    DOI: 10.1016/j.amc.2024.129252
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324007136
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.129252?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Chuin-Shan & Noorizadegan, Amir & Young, D.L. & Chen, C.S., 2023. "On the selection of a better radial basis function and its shape parameter in interpolation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    2. Hosseinzadeh, Hossein & Shirzadi, Ahmad, 2023. "On optimal radius of sub-domains in meshless LBIE method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 145-160.
    3. Assari, Pouria & Dehghan, Mehdi, 2017. "A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 424-444.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Assari, Pouria & Dehghan, Mehdi, 2019. "A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 249-265.
    2. Liu, Tao & Soleymani, Fazlollah & Ullah, Malik Zaka, 2024. "Solving multi-dimensional European option pricing problems by integrals of the inverse quadratic radial basis function on non-uniform meshes," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Kumhar, Raju & Kundu, Santimoy & Pandit, Deepak Kr. & Gupta, Shishir, 2020. "Green’s function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    4. Akbari, Tahereh & Esmaeilbeigi, Mohsen & Moazami, Davoud, 2024. "A stable meshless numerical scheme using hybrid kernels to solve linear Fredholm integral equations of the second kind and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 1-28.
    5. Xu, Fei & Huang, Qiumei, 2019. "An accurate a posteriori error estimator for semilinear Neumann problem and its applications," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    6. Radoslaw Stanislawski & Jules-Raymond Tapamo & Marcin Kaminski, 2023. "Virtual Signal Calculation Using Radial Neural Model Applied in a State Controller of a Two-Mass System," Energies, MDPI, vol. 16(15), pages 1-23, July.
    7. Pan, Yubin & Huang, Jin & Ma, Yanying, 2019. "Bernstein series solutions of multidimensional linear and nonlinear Volterra integral equations with fractional order weakly singular kernels," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 149-161.
    8. Noorizadegan, A. & Young, D.L. & Hon, Y.C. & Chen, C.S., 2024. "Power-enhanced residual network for function approximation and physics-informed inverse problems," Applied Mathematics and Computation, Elsevier, vol. 480(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:493:y:2025:i:c:s0096300324007136. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.