Topic
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 results suggest that the accuracy of NSFnets, for both laminar and turbulent flows, can be improved with proper tuning of weights (manual or dynamic) in the loss function.
303 citations
TL;DR: The method of finite spheres as discussed by the authors is a special case of the meshless local Petrov-Galerkin (MLPG) procedure, where the nodes are placed and the numerical integration is performed without a mesh.
Abstract: The objective of this paper is to present some of our recent developments in meshless methods In particular, a technique is given – the method of finite spheres – that is truly meshless in nature in the sense that the nodes are placed and the numerical integration is performed without a mesh The method can be viewed as a special case of the general formulation known as the meshless local Petrov–Galerkin (MLPG) procedure Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated A new way of modeling doubly-connected domains is also presented Various example problems are solved to demonstrate the method
300 citations
TL;DR: In this paper, the authors considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximate functions and their derivatives and showed a moderate improvement in the accuracy of the smoothed interpolant.
261 citations
TL;DR: In this paper, a numerical procedure based on material point method (MPM) is proposed to solve fully coupled dynamic problems that undergo large deformations in saturated soils, where two sets of Lagrangian material points are used to represent soil skeleton and pore water layers.
260 citations
TL;DR: In this paper, the implementation of h-adaptivity for mesh-free particle methods within a structured framework is described, where the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions.
Abstract: The implementation of h-adaptivity for meshfree particle methods within a structured framework is described In this framework, the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions The advantage of meshfree approximations in this framework lies in the ease of implementing h-adaptivity and the simplicity of the data structures Particles can easily be added and removed without complications in the data structure, although there are some issues in the quadrature An a posteriori error estimation is used for the adaptive refinement An adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities Several non-linear examples are also given Copyright © 2005 John Wiley & Sons, Ltd
254 citations