The dimension split element-free Galerkin method for three-dimensional potential problems

Meng, Zhijuan; Cheng, Heng; D., L.; Cheng, Yumin

doi:10.1007/s10409-017-0747-7

Cited by 43 publications

(11 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that the number of planes in the direction x 1 should be large. In this numerical example, we choose the number of planes to be 30,35,40,45, and the corresponding results are shown in Figure 14. From the results, we can see that the results converge as the number of planes increase, and the DSRKPM has obvious advantages of computational efficiency.…”

Section: Figure 14mentioning

confidence: 99%

“…35 Cheng et al combined the DSM with improved complex variable EFG method to solve 3D potential problems, 36 wave propagation problems, 37 3D transient heat conduction problems, 38 and advection-diffusion problems. 39 Meng et al combined the DSM with IEFG method to solve 3D potential problems, 40 wave propagation problems, 41 and transient heat conduction problems. 42 In this paper, introducing the DSM into the RKPM, a new method that is the DSRKPM for 3D potential problems is presented.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Peng

Cheng

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three‐dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two‐dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element‐free Galerkin method for 3D potential problems.

show abstract

Section: Figure 14mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Peng

Cheng

2019

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…By combining the dimension splitting method and meshless methods, the hybrid complex variable EFG method [27][28][29][30][31], the dimension split EFG method [32][33][34][35], and the dimension splitting reproducing kernel particle method [36] for 3D problems are proposed, respectively, and those new methods can improve the computational speed of traditional meshless methods for solving 3D problems greatly.…”

Section: Introductionmentioning

confidence: 99%

Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

Cheng

Guo-dong

2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, the improved element-free Galerkin (IEFG) method is used for solving 3D advection-diffusion problems. The improved moving least-squares (IMLS) approximation is used to form the trial function, the penalty method is applied to introduce the essential boundary conditions, the Galerkin weak form and the difference method are used to obtain the final discretized equations, and then the formulae of the IEFG method for 3D advection-diffusion problems are presented. The error and the convergence are analyzed by numerical examples, and the numerical results show that the IEFG method not only has a higher computational speed but also can avoid singular matrix of the element-free Galerkin (EFG) method.

show abstract

The dimension split element-free Galerkin method for three-dimensional potential problems

Cited by 43 publications

References 40 publications

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

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

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

Analyzing 3D Advection-Diffusion Problems by Using the Improved Element-Free Galerkin Method

Contact Info

Product

Resources

About