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New Trends on Meshless Method and Numerical Analysis

Submission Deadline: 31 December 2024 Submit to Special Issue

Guest Editors

Prof. Ji Lin, Hohai University, China
Prof. Fajie Wang, Qingdao University, China

Summary

In recent years, in the category of numerical analysis, the meshless method has witnessed a research boom to free engineers and scientists from the difficult task of mesh generation and to reduce mesh sensitivity of solutions. Meshless methods include the kernel methods, the moving least square method, the radial basis functions, etc, such as the well-known smoothed particle hydrodynamics, the diffuse element method, the element-free Galerkin, the method of fundamental solution, the reproducing kernel particle method. The meshless method has become an attractive alternative for problems in computational mechanics, computational physics, computational chemistry, computational biology, computational materials science, etc.

The main target of this special issue is to focus on the latest developments of meshless methods, such as theoretical analysis, applications, development of new methods, fast solution techniques, etc. The applications of advanced techniques such as isogeometric analysis, artificial intelligence, the physical-based numerical model, etc, in meshless methods are also welcomed.


Keywords

Meshless method, Boundary-type meshless method, Localized meshless method, Fast algorithm, Domain-type meshless method, Isogeometric analysis, Artificial intelligence, Physical-based numerical model, Theoretical analysis, Applications

Published Papers


  • Open Access

    ARTICLE

    Sub-Homogeneous Peridynamic Model for Fracture and Failure Analysis of Roadway Surrounding Rock

    Shijun Zhao, Qing Zhang, Yusong Miao, Weizhao Zhang, Xinbo Zhao, Wei Xu
    CMES-Computer Modeling in Engineering & Sciences, DOI:10.32604/cmes.2023.045015
    (This article belongs to this Special Issue: New Trends on Meshless Method and Numerical Analysis)
    Abstract The surrounding rock of roadways exhibits intricate characteristics of discontinuity and heterogeneity. To address these complexities, this study employs non-local Peridynamics (PD) theory and reconstructs the kernel function to represent accurately the spatial decline of long-range force. Additionally, modifications to the traditional bond-based PD model are made. By considering the micro-structure of coal-rock materials within a uniform discrete model, heterogeneity characterized by bond random pre-breaking is introduced. This approach facilitates the proposal of a novel model capable of handling the random distribution characteristics of material heterogeneity, rendering the PD model suitable for analyzing the deformation and failure of heterogeneous layered… More >

  • Open Access

    ARTICLE

    Optimal Shape Factor and Fictitious Radius in the MQ-RBF: Solving Ill-Posed Laplacian Problems

    Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang
    CMES-Computer Modeling in Engineering & Sciences, DOI:10.32604/cmes.2023.046002
    (This article belongs to this Special Issue: New Trends on Meshless Method and Numerical Analysis)
    Abstract To solve the Laplacian problems, we adopt a meshless method with the multiquadric radial basis function (MQ-RBF) as a basis whose center is distributed inside a circle with a fictitious radius. A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function. A sample function is interpolated by the MQ-RBF to provide a trial coefficient vector to compute the merit function. We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm. The novel method provides the optimal values of parameters and,… More >

  • Open Access

    ARTICLE

    A Novel Method for Linear Systems of Fractional Ordinary Differential Equations with Applications to Time-Fractional PDEs

    Sergiy Reutskiy, Yuhui Zhang, Jun Lu, Ciren Pubu
    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1583-1612, 2024, DOI:10.32604/cmes.2023.044878
    (This article belongs to this Special Issue: New Trends on Meshless Method and Numerical Analysis)
    Abstract This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations (PDEs). The modified radial basis… More >

  • Open Access

    ARTICLE

    An Efficient Local Radial Basis Function Method for Image Segmentation Based on the Chan–Vese Model

    Shupeng Qiu, Chujin Lin, Wei Zhao
    CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.1, pp. 1119-1134, 2024, DOI:10.32604/cmes.2023.030915
    (This article belongs to this Special Issue: New Trends on Meshless Method and Numerical Analysis)
    Abstract In this paper, we consider the Chan–Vese (C-V) model for image segmentation and obtain its numerical solution accurately and efficiently. For this purpose, we present a local radial basis function method based on a Gaussian kernel (GA-LRBF) for spatial discretization. Compared to the standard radial basis function method, this approach consumes less CPU time and maintains good stability because it uses only a small subset of points in the whole computational domain. Additionally, since the Gaussian function has the property of dimensional separation, the GA-LRBF method is suitable for dealing with isotropic images. Finally, a numerical scheme that couples GA-LRBF… More >

    Graphic Abstract

    An Efficient Local Radial Basis Function Method for Image Segmentation Based on the Chan–Vese Model

  • Open Access

    ARTICLE

    An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

    Ziqiang Bai, Wenzhen Qu, Guanghua Wu
    CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.3, pp. 2955-2972, 2024, DOI:10.32604/cmes.2023.031474
    (This article belongs to this Special Issue: New Trends on Meshless Method and Numerical Analysis)
    Abstract In the past decade, notable progress has been achieved in the development of the generalized finite difference method (GFDM). The underlying principle of GFDM involves dividing the domain into multiple sub-domains. Within each sub-domain, explicit formulas for the necessary partial derivatives of the partial differential equations (PDEs) can be obtained through the application of Taylor series expansion and moving-least square approximation methods. Consequently, the method generates a sparse coefficient matrix, exhibiting a banded structure, making it highly advantageous for large-scale engineering computations. In this study, we present the application of the GFDM to numerically solve inverse Cauchy problems in two-… More >

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