scispace - formally typeset
Search or ask a question
Topic

Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction-diffusion systems, where the thin plate splines (TPS) are used as the basis functions and a simple predictor-corrector (P-C) scheme is performed.
Abstract: In the present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of pattern formation in nonlinear reaction-diffusion systems. Firstly, we obtain a time discrete scheme by approximating the time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The effect of parameters and conditions are studied by considering the well known Brusselator model. Two test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed scheme.

1 citations

Journal ArticleDOI
TL;DR: Wang et al. as discussed by the authors proposed an improvement scheme for nodal integration for truly meshless methods, which transformed the integration area to a circle and then numerically integrated it to improve stabilization and accuracy.
Abstract: Meshless methods, developed in various ways over the past decade, have been attractive as new computational methods in that they do not need mesh generation in analyzing procedure. But most of these methods were not truly meshless methods because background meshes were required for the spatial integration of a weak form. Accordingly, in this paper, nodal integration for truly meshless methods has been studied, and an improvement scheme is proposed. To improve stabilization and accuracy, which are the weak points in previous nodal integration methods, the integration area is transformed to circle and then numerically integrated. This method does not need any adding term for stabilization in the variational formulation and then simplifies the integration procedure. Numerical test results show that the proposed method is more accurate, stable, and reasonable than the existed nodal integration methods.

1 citations

Journal Article
Liu Yan1
TL;DR: The idea in this study could be generally extended to other methods with integral mesh, and transformed them to be truly meshless.
Abstract: Meshless methods were preponderant in dealing with problems when it was difficult to employ finite element method.And they could simplify pre-and post-processings.Element-free Galerkin method(EFG),based on moving least squares method(MLS),was one of the meshless methods.Owing to its accuracy and stability,EFG method was widely applied in structure and seepage analysis.However,EFG method was not a "truly" meshless method,since mesh was still used to conduct numerical integration.A Monte Carlo-based EFG method(MCEFG) was proposed to do the integration with Monte Carlo method.The mesh or cell was not used in MCEFG method.So it was truly a meshless method.A program based on MCEFG method was compiled and applied to seepage analysis.It was shown that the method was suitable for simulating seepage with a free surface.The idea in this study could be generally extended to other methods with integral mesh,and transformed them to be truly meshless.

1 citations

Journal ArticleDOI
TL;DR: In this paper , the impact dynamics equations are solved by the meshless approach (MLPG5), both stress as well as displacements are interpolated, through the moving least squares (MLS) interpolation schemes, which eliminates the expensive process of domain integrals and differentiating the shape function.
Abstract: The ‘Mixed’ Meshless Local Petrov-Galerkin Finite Volume method (MLPG5) is developed for solving low-velocity impact problems of plastic bonded explosives (PBX). Due to the ductility and plasticity of PBX, there is large deformation instead of pulverization or fragmentation. In this paper, the impact dynamics equations are solved by the meshless approach (MLPG5), both stress as well as displacements are interpolated, through the moving least squares (MLS) interpolation schemes, which eliminates the expensive process of domain integrals and differentiating the shape function. The collocation method is applied to enforce strain-displacement relationships only at each nodal point, instead of the subdomain. In the present mixed method, the independent interpolation of stress improves accuracies of both the plastic stress and contact stress. The contact force is obtained by penalty function method via iteration scheme. Due to the non-linear constitutive relation, the incremental stress is obtained via radial return schemes through Newton Raphson iteration. Finally, several numerical examples are given to demonstrate the feasibility and the accuracy of the present numerical approach compared with the finite element method. Numerical examples also demonstrate the advantages of the present methods: (i) smaller support sizes can be used; (ii) higher accuracies of stress are obtained.

1 citations

Journal ArticleDOI
TL;DR: VDLSM as a new, straightforward and easy applicable method has been suggested here for overcoming deficiency using the algorithm of the Voronoi tessellation for constructing the Moving Least Squares (MLS) shape functions.
Abstract: A new approach in meshless methods has been introduced for stress assessment around a crack in two-dimensional elastic solids. This method with the name VDLSM (Voronoi Based Discrete Least Squares Meshless) is a pure meshless method which does not implement nodal mesh for trial and test functions. Rather, it uses a collection of the scattered nodal points and implements the discrete least squares approach to discretize the strong form of the governing differential equations on the domain of interest. This can reduce considerably the pre-processing cost of the analysis. Meshless methods generally are faced with some difficulty to accommodate the stress analysis in the vicinity of sharply concave surfaces such as cracks. Some techniques have been used to fix that problem such as visibility, transparency and diffraction, but these methods require some additional back corrective analyses for those parts of the domain located near the crack, which lengthen the time consumed for the solution and, moreover, do not provide the desired accuracy for the unknowns in these regions. VDLSM as a new, straightforward and easy applicable method has been suggested here for overcoming such deficiency using the algorithm of the Voronoi tessellation for constructing the Moving Least Squares (MLS) shape functions.

1 citations


Network Information
Related Topics (5)
Finite element method
178.6K papers, 3M citations
89% related
Numerical analysis
52.2K papers, 1.2M citations
86% related
Discretization
53K papers, 1M citations
86% related
Boundary value problem
145.3K papers, 2.7M citations
82% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897