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Meshfree methods

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


Papers
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Journal ArticleDOI
01 Sep 2016
TL;DR: In this paper, the authors deal with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using mesh-free method and a numerical algorithm based on element free Galerkin method is developed.
Abstract: The present study deals with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using meshfree method. A numerical algorithm based on Element free Galerkin method is developed. A one dimensional form of the advective-diffusive transport equation for homogeneous and stratified soil is considered for the analysis using irregular nodes. A FORTRAN program is developed to obtain numerical solution and the results are validated with the available results in the literature. A detailed parametric study is conducted to examine the effect of certain key parameters. Effect of change of dispersion, velocity, porosity, distribution coefficient and thickness of layer is studied on the concentration of the contaminant

1 citations

Journal Article
TL;DR: The basic principle of meshless methods, a newly developed numerical computation method which is similar to FEM, is discussed in detail and the prospect about meshless method is speculated.
Abstract: Meshless method is a newly developed numerical computation method which is similar to FEM The basic principle of meshless methods is discussed in detail The features of some major meshless methods are analyzed Finally the prospect about meshless method is speculated

1 citations

Journal ArticleDOI
TL;DR: In this article, the concept of the numerical Green's function (NGF) idea for elastostatic fracture mechanics using the boundary element-free method (BEFM) was introduced.
Abstract: This work aims at introducing the concept of the numerical Green’s function (NGF) idea for elastostatic fracture mechanics using the boundary element-free method (BEFM). Unlike the local boundary integral equation method (LBIE), the BEFM only requires boundary interpolation. This method derives from the coupling of the boundary integral equation method and the orthogonal moving least-squares approximation scheme (OMLS). OMLS differs from standard MLS by using an orthogonal basis instead of only a linear independent one, which increases its accuracy and efficiency. Some illustrative examples are included in the end.

1 citations

Book ChapterDOI
01 Jan 2017
TL;DR: This chapter explores an alternative approach through the use of meshless methods for element-free Galerkin (EFG) approach, which is based on a distribution of nodes, within a domain, which are not required to be interconnected.
Abstract: The microstructure of composite materials is often distinguished by the size, shape and distribution of the reinforcing constituents. Various analytical, semi-analytical and computational approaches have been developed to determine their effective properties and to study the evolution of damage in these materials. The finite element method (FEM) has emerged as the primary computational tool for micromechanical modelling, particularly for composites with complex microstructures or architecture. Nonetheless, the meshing of complex geometries may present difficulties. This is compounded by the challenge of modelling the propagation of cracks in heterogeneous materials. While the eXtended Finite Element Method (XFEM) mitigates the need for re-meshing, by incorporating enrichment functions in the finite element formulation to permit the propagation of cracks through an element, this chapter explores an alternative approach through the use of meshless methods. Such methods are based on a distribution of nodes, within a domain, which are not required to be interconnected. A number of these methods have been proposed over recent years and the element-free Galerkin (EFG) approach has been adopted in the work presented. This chapter introduces the basic concepts of the EFG method and is followed by an example of the use of the EFG method for constructing a representative volume element (RVE) of a composite material from which homogenised elastic properties are determined. A numerical strategy is subsequently proposed for propagating a crack through these composites, followed by the more complex case of propagating multiple interacting cracks, to yield insight into the formation of microscale damage.

1 citations

Proceedings ArticleDOI
17 Sep 2010
TL;DR: In this article, the authors developed efficient mesh free methods to solve European and American option pricing problems using radial basis functions, these methods leads to systems of difference equations which are solved by using a θ-method.
Abstract: We develop efficient mesh free methods to solve European and American option pricing problems. Using radial basis functions, these methods leads to systems of difference equations which are solved by using a θ‐method. Numerical results describing the payoff functions and option values are also presents.

1 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897