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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.
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TL;DR: The meshless local Petrov-Galerkin method (MLPG) as discussed by the authors is a local weak formulation of the equilibrium equations, where meshless shape functions are constructed using randomly scattered set of points without any relation between points.
Abstract: Abstract The paper deals with use of the meshless method for soil bearing capacity analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) - local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The Heaviside step function is test function used in the meshless implementation presented in the article. Heaviside test function makes weak formulation integral very simple, because only body integral in governing equation is due a body force.
01 Jan 2008
TL;DR: The aim of this contribution is a numerical study of the accuracy and convergence properties of the method when applied to different kind of PDEs with known analytical solutions.
Abstract: We present a Space-Time Meshfree Collocation Method based on Interpolating Moving Least Squares (STMCM-IMLS). The Moving Least Squares (MLS) technique and its interpolating counterpart (IMLS), introduced in [2] for scattered data approximation and interpolation respectively, are the basis for most of the meshfree methods, i.e. methods which use only a set of points without a node-tonode connectivity to find numerical solutions of partial differential equations. The meshfree collocation method based on IMLS was introduced by authors in primary studies [3, 4]. The idea of the Space-Time Meshfree Collocation Method (ST-MCM) was presented in [5], and applied to tracking the evolution of dynamic interfaces under heavy deformations by level-set method in [6]. The aim of this contribution is a numerical study of the accuracy and convergence properties of the method when applied to different kind of PDEs with known analytical solutions. We investigate the time discretization properties by solving ordinary differential equations, the discretization in space solving an elliptic (parabolic) model problem, and end up by showing the numerical properties of the method when applied to hyperbolic PDEs.
01 Jan 2002
TL;DR: In this article, the authors compared the performance of the h-and-lor p-adaptation, boundary elements, and meshless methods for solving heat transfer problems and found that the h andlor padaptation method has its merits and deficiencies.
Abstract: the web site http:llwww.unlv.edulResearch CentedNCACM. method has its merits and deficiencies. Additional infomation can be found on element and meshless methods for several heat transfer test problems. Each finite element scheme that employs h-adaptation are compared with boundary schemes that are especially promising. In this study, solutions obtained using a (h- andlor p-adaptation), boundary elements, and meshless methods are three modeling community. Finite element methods that use some form of adaptation numerical techniques have become particularly attractive and of interest to the While many numerical schemes exist for solving heat transfer problems, several
01 Dec 2010
TL;DR: DEM is constructed by Reproducing Kernel Partical Method based on the discrete points in YunNan area and Gauss Synthetic Surface and the quality of constructed DEM is analyzed based on RMSE shows that the accuracy of DEM constructed by meshfree method is acceptable, and it is mesh free.
Abstract: Meshfree method is a new numeric method which is evolved from Finite Element Method (FEM). It obtains remarkable achievements in computational mechanics fields. It can solve special problems which can't be solved by FEM. Grid is not needed when scattering research area. This is the most significant characteristic of meshfree method compared with FEM. In this paper DEM is constructed by Reproducing Kernel Partical Method based on the discrete points in YunNan area and Gauss Synthetic Surface. And the quality of constructed DEM is analyzed based on RMSE. The result shows that the accuracy of DEM constructed by meshfree method is acceptable, and it is mesh free.
TL;DR: In this paper , a concurrent multiscale method based on the maximum entropy statistical method is proposed for the analysis of amorphous materials, which is expected to perform efficiently because of its entropic and irregular intrinsic.