The dimension splitting reproducing kernel particle method for three‐dimensional potential problems

Peng, Piaopiao; Wu, Qiang; Cheng, Yumin

doi:10.1002/nme.6203

Cited by 41 publications

(11 citation statements)

References 41 publications

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“…By combining meshless methods and the finite difference method, the hybrid CVEFG method [52][53][54][55][56], dimension-splitting EFG method [57][58][59][60], dimension-splitting reproducing kernel particle method [61][62][63][64], interpolating dimension-splitting EFG method [65] and hybrid generalized interpolated EFG method [66] were proposed. These methods can greatly improve the computational efficiency of the traditional meshless method for solving multi-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Cheng

Peng

2021

Mathematics

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The improved element-free Galerkin (IEFG) method is proposed in this paper for solving 3D Helmholtz equations. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty technique is used to enforce the essential boundary conditions. Thus, the final discretized equations of the IEFG method for 3D Helmholtz equations can be derived by using the corresponding Galerkin weak form. The influences of the node distribution, the weight functions, the scale parameters of the influence domain, and the penalty factors on the computational accuracy of the solutions are analyzed, and the numerical results of three examples show that the proposed method in this paper can not only enhance the computational speed of the element-free Galerkin (EFG) method but also eliminate the phenomenon of the singular matrix.

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Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Cheng

Peng

2021

Mathematics

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“…Numerical calculations are widely used in scientific research and engineering applications [23][24][25], which can realize optimal design and high-precision analysis of structures. A new and effective numerical method developed in recent years is the meshless method, including diffuse element method [26], smoothed particle method [27], reproducing kernel particle method [28][29][30][31], elementfree Galerkin method [32][33][34][35][36][37][38][39][40][41], finite point method [42], natural element method [43], radial basis function method [44], mesh-free kp-Ritz method [45], complex variable meshless method [46][47][48], and all kinds of meshless boundary integral equation method [49][50][51]. In addition, numerical methods also include weighted residual method, finite difference method, finite element method, and boundary element method.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Optimization of Pulling Point Position of Luffing Jib on Portal Crane

Jiao

Qin

Han³

et al. 2021

Mathematical Problems in Engineering

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Portal crane is the most commonly used equipment for cargo handling of large mixed loading ships with its advantages of flexible and convenient operation, wide adaptability, and high loading and unloading efficiency. The reasonable modeling and optimization of the pulling point position of luffing jib of portal crane can reduce the rack force of portal crane and the power consumption output of the rack and pinion during the luffing process. Based on penalty function optimization, the interior point method is used to optimize the pulling point position of luffing jib. Compared with the initial design, the race force of the luffing jib is reduced to a certain extent. In addition, the consistency between the finite element analysis results and the optimization results can be verified, and the effectiveness of the optimization design is also proved through the finite element analysis of portal crane.

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“…Cheng et al proposed the improved moving least-squares (IMLS) approximation to develop the improved element-free Galerkin (IEFG) method [33][34][35] and the interpolating element-free Galerkin method [36][37][38]. By introducing the dimension splitting method into the reproducing kernel particle method, a new meshless method was developed to solve three-dimensional potential problems [39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

Guo

Boldbaatar

et al. 2020

Mathematical Problems in Engineering

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This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. Based on the local Petrov–Galerkin formulation and the center difference method for time discretization, a system of nonlinear discrete equations is obtained. The numerical examples are presented and the numerical solutions are found to be in good agreement with the results in the literature to validate the ability of the present meshless method to handle the 2 + 1-dimensional sine-Gordon equation related problems.

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The dimension splitting reproducing kernel particle method for three‐dimensional potential problems

Cited by 41 publications

References 41 publications

The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Modeling and Optimization of Pulling Point Position of Luffing Jib on Portal Crane

Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

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