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: A multilevel algorithm is suggested that effectively finds a near-optimal shape parameter in the meshless Gaussian radial basis function finite difference method, which helps to significantly reduce the error.
Abstract: We investigate the influence of the shape parameter in the meshless Gaussian radial basis function finite difference (RBF-FD) method with irregular centres on the quality of the approximation of the Dirichlet problem for the Poisson equation with smooth solution. Numerical experiments show that the optimal shape parameter strongly depends on the problem, but insignificantly on the density of the centres. Therefore, we suggest a multilevel algorithm that effectively finds a near-optimal shape parameter, which helps to significantly reduce the error. Comparison to the finite element method and to the generalised finite differences obtained in the flat limits of the Gaussian RBF is provided.
68 citations
TL;DR: In this paper, a thin shell analysis from scattered points with maximum-entropy approximants is presented, where the maximum entropy approximation of the shell is used to estimate the maximum number of points in the shell.
Abstract: This is the accepted version of the following article: [Millan, D., Rosolen, A. and Arroyo, M. (2011), Thin shell analysis from scattered points with maximum-entropy approximants. Int. J. Numer. Meth. Engng., 85: 723–751. doi:10.1002/nme.2992], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.2992/abstract
68 citations
TL;DR: In this article, a simple classical radial basis functions (RBFs) collocation (Kansa) method was proposed for numerical solution of the coupled Korteweg-de Vries (KdV) equations, coupled Burgers' equations, and quasi-nonlinear hyperbolic equations.
Abstract: This paper formulates a simple classical radial basis functions (RBFs) collocation (Kansa) method for the numerical solution of the coupled Korteweg-de Vries (KdV) equations, coupled Burgers’ equations, and quasi-nonlinear hyperbolic equations. Contrary to the mesh oriented methods such as the finite-difference and finite element methods, the new technique does not require mesh to discretize the problem domain, and a set of scattered nodes provided by initial data is required for realization of solution of the problem. Accuracy of the method is assessed in terms of the error norms L 2 , L ∞ , number of nodes in the domain of influence, time step length, parameter free and parameter dependent RBFs. Numerical experiments are performed to demonstrate the accuracy and robustness of the method for the three classes of partial differential equations (PDEs).
67 citations
TL;DR: In this paper, the authors demonstrate that the element-free Galerkin (EFG) method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2D elasticity.
66 citations
TL;DR: In this paper, a computational methodology of a micromechanics cell model is proposed to establish the constitutive law during material fracture, which is applied to numerical examples including necking behavior of a tensile bar, a cracked panel under tension, an edge notched panel under pure bending, a plane strain plate under compression, and the ductile tearing with large deformation of a notch-bend specimen.
66 citations