Improvements to the meshless generalized finite difference method

Kamyabi, Ata; Kermani, Vahid; Kamyabi, Mohammadmahdi

doi:10.1016/j.enganabound.2018.11.002

Cited by 18 publications

(6 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Arteaga et al [18] showed that static diffusion equation model could be solved by using finite difference method. For more theories and further applications, the modified (generalized) finite difference method was investigated by some researchers, such as Kamyabi et al [19]. This modified (generalized) finite difference method has been applied in many areas, such as in analyzing matched layer elements [20], solving plane crack problem [21], analyzing dendritic growth [22], numerical simulation on waves-current interactions [23], and analyzing three-dimensional transient electromagnetic problems [24].…”

Section: Introductionmentioning

confidence: 99%

Analysis of wastewater facultative pond using advection-diffusion model based on explicit finite difference method

Sunarsih

Sasongko

Sutrisno

et al. 2020

Environmental Engineering Research

View full text Add to dashboard Cite

This paper describes an advection-diffusion mathematical model in facultative ponds of different geometrical domains. The geometrical domains of the facultative ponds are the side (one-dimensional), the plane (two-dimensional), and the space (three-dimensional). The purpose of this paper is to know the numerical simulations of these three advection-diffusion models (1D, 2D, and 3D) using explicit finite difference method. Numerical simulation can be used to evaluate the distribution of pollutant concentrations. The concentration of pollutant tested was same as the concentration of biochemical oxygen demand. The result of numerical simulation showed that more complex the geometrical domain of a facultative pond, the more visible is the process of moving the mass concentration (advection) and mass spread (diffusion) in the facultative ponds.

show abstract

Section: Introductionmentioning

confidence: 99%

Analysis of wastewater facultative pond using advection-diffusion model based on explicit finite difference method

Sunarsih

Sasongko

Sutrisno

et al. 2020

Environmental Engineering Research

View full text Add to dashboard Cite

show abstract

“…The influence of factors such as the size of the point cluster, the shape of the point cluster, and the selection of the weight function on the accuracy of the GFDM is also analyzed [11]. Kamyabi proposed an improved version of the GFDM, which makes it no longer dependent on the least square method and can handle the Neumann boundary conditions in a sophisticated way [12]. At present, the GFDM has been effectively applied in many fields.…”

Section: Introductionmentioning

confidence: 99%

Generalized Finite Difference Method for Solving Waveguide Eigenvalue Problems

Bao

2022

ACES Journal

View full text Add to dashboard Cite

The generalized finite difference method (GFDM) is a meshless method that has become popular in recent years. The basic theory underlying GFDM is to expand the point cluster function value at the center node by Taylor’s formula and then obtain the best linear combinations of these function values to represent the derivative at the central node by the least square fitting technique. Subsequently, the minimized weighted error between the approximated value and the accurate value is obtained. This paper establishes the general steps for solving waveguide eigenvalue problems with GFDM. Excellent performance is shown by comparing the proposed method and other common solutions. The robustness of the proposed method is verified by calculating the cutoff wavenumbers of typical waveguides and the eccentric circular waveguide in different modes.

show abstract

“…In recent years, many efforts have been devoted to generalize the traditional difference method on scattered point sets. Most of them are based on a large number of neighboring points to fit derivatives [13][14][15][16], while there are also a few jobs in which a small number of neighbors are employed [17][18][19], however, none of them can address the issue of singularity or ill-conditioning of numerical derivatives at the fundamental level. In addition, many scholars have studied the difference method based on radial basis function (RBF) [20][21][22][23][24], which can be also viewed as a generalization of the traditional difference method.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Analyses on Discrete Formulae of Directional Differentials in the Finite Point Method

Shen¹

2022

JCM

View full text Add to dashboard Cite

Improvements to the meshless generalized finite difference method

Cited by 18 publications

References 30 publications

Analysis of wastewater facultative pond using advection-diffusion model based on explicit finite difference method

Analysis of wastewater facultative pond using advection-diffusion model based on explicit finite difference method

Generalized Finite Difference Method for Solving Waveguide Eigenvalue Problems

Theoretical Analyses on Discrete Formulae of Directional Differentials in the Finite Point Method

Contact Info

Product

Resources

About