A new meshless local integral equation method

Hosseinzadeh, Hossein; Shirzadi, Ahmad

doi:10.1016/j.apnum.2023.08.007

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…The complete calculation process of the shape function Ψ(x (k) ) has been provided in much of the literature [8] and will not be elaborated on here. Only the selection of the basis function and weight function is given.…”

Section: The Hrkpm Scheme For 3d Helmholtz Equationmentioning

confidence: 99%

“…An alternate strategy is the meshless technique, which may successfully handle some challenging issues related to mesh distortion by using a set of discrete points [4]. After decades of unremitting research by researchers, many meshless methods have emerged [5][6][7][8]. In order to facilitate the comparison of the advantages and disadvantages of various meshless methods, many widely used meshless algorithms have been compared and summarized in certain review studies [9,10].…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

Peng,

Wang,

Cheng

2024

Mathematics

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The reproducing kernel particle method (RKPM) is one of the most universal meshless methods. However, when solving three-dimensional (3D) problems, the computational efficiency is relatively low because of the complexity of the shape function. To overcome this disadvantage, in this study, we introduced the dimension splitting method into the RKPM to present a hybrid reproducing kernel particle method (HRKPM), and the 3D Helmholtz equation is solved. The 3D Helmholtz equation is transformed into a series of related two-dimensional (2D) ones, in which the 2D RKPM shape function is used, and the Galerkin weak form of these 2D problems is applied to obtain the discretized equations. In the dimension-splitting direction, the difference method is used to combine the discretized equations in all 2D domains. Three example problems are given to illustrate the performance of the HRKPM. Moreover, the numerical results show that the HRKPM can improve the computational efficiency of the RKPM significantly.

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Section: The Hrkpm Scheme For 3d Helmholtz Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

Peng,

Wang,

Cheng

2024

Mathematics

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An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order

Taghipour,

Shirzadi,

Safarpoor

2023

J Nonlinear Math Phys

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The subject of this paper is to propose a numerical algorithm for solving 2D diffusion and diffusion-wave equations of distributed order fractional derivatives. Such equations arise in modelling complex systems and have many important applications. Existence of integral term over the order of fractional derivative causes the high complexity of these equations and so their numerical solutions needs special cares. Using Gauss quadrature approach for discretizing the integral term of fractional derivative converts the distributed equation into a multi-term fractional differential equation. Then, the time variable is discretized with a suitable finite difference approach. The resultant semi-discretized equations are fully discretized by a radial basis function-generated finite difference based method. Convergence of the method are studied numerically. Various kind of test problems are considered for a comprehensive numerical study and the results confirm the efficiency of the method.

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Numerical treatment of multi-dimensional time-fractional Benjamin-Bona-Mahony-Burgers equations in arbitrary domains with a novel improvised RBF-based method

Lin,

Shi,

Reutskiy

et al. 2024

Computers & Mathematics with Applications

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A new meshless local integral equation method

Cited by 4 publications

References 27 publications

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Helmholtz Equation

An RBF-FD Method for Numerical Solutions of 2D Diffusion-Wave and Diffusion Equations of Distributed Fractional Order

Numerical treatment of multi-dimensional time-fractional Benjamin-Bona-Mahony-Burgers equations in arbitrary domains with a novel improvised RBF-based method

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