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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: In this paper, the authors presented meshless overlapping Schwarz additive and multiplicative domain decomposition schemes for time-dependent problems using radial basis functions by solving an unsteady convection-diffusion problem for various Peclet numbers.
Abstract: In this article, we present meshless overlapping Schwarz additive and multiplicative domain decomposition schemes for time-dependent problems using radial basis functions. The proposed schemes are compared with the global radial basis function collocation method and an explicit multizone domain decomposition method (Wong et al., Comput Math Appl 37 (1999), 23–43) by solving an unsteady convection-diffusion problem for various Peclet numbers. Stability analysis of the presented schemes suggest that for radial basis functions incorporating a free shape parameter, the freedom of varying the shape parameter decreases with increase in the number of collocation points. Numerical studies show that the ill-conditioning problem of global radial basis function collocation method is reduced by the proposed Schwarz schemes. Also, with an increase in the number of subdomains the efficiency of the Schwarz schemes increases with a slight loss in the accuracy. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

18 citations

Journal ArticleDOI
TL;DR: In this article, a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM, which is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set-up.
Abstract: The element-free Galerkin method (EFG) and the natural element method (NEM) are two well known and widely used meshless methods. Whereas the EFG method can represent moving boundaries like cracks only by modifying the weighting functions the NEM requires an adaptation of the nodal set-up. But on the other hand the NEM is computationally more efficient than EFG. In this paper a new concept for the automatic adjustment of nodal influence domains in the EFG method is presented in order to obtain an efficiency similar to the NEM. This concept is based on the definition of natural neighbours for each meshless node which can be determined from a Voronoi diagram of the nodal set-up. In this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction. In the paper we show that this concept leads, especially for problems with grading node density, to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort. Copyright © 2006 John Wiley & Sons, Ltd.

18 citations

Journal ArticleDOI
TL;DR: The application of the natural element method (NEM) to solve inelastic finite deformation problems in isotropic and fiber-reinforced materials and the α-NEM extension generalizes this behavior to non-convex boundaries is presented.

18 citations

Journal ArticleDOI
TL;DR: In this article, a geometrically nonlinear analysis of flat, curved and folded shells under finite rotations is performed by enhanced six degrees of freedom (6-DOFs) mesh-free formulation.
Abstract: Geometrically nonlinear analysis of flat, curved and folded shells under finite rotations is performed by enhanced six degrees of freedom (6-DOFs) meshfree formulation. Curvilinear surfaces are dealt with the concept of convected coordinates. Equilibrium equations are derived by total Lagrangian formulation with Green–Lagrange strain and Second Piola–Kirchhoff stress. Both shell geometry and its deformation are approximated by Reproducing Kernels (RKs). Transverse shear strains are considered by Mindlin–Reissner theory. Numerical integration of the stiffness matrix is estimated by using the Stabilized Conforming Nodal Integration (SCNI) method. To show accuracy and effectiveness of the proposed formulation and discretization, benchmark problems from the literatures are considered. Apart from reference solutions available in the literature, additional reference results based on finite element method (FEM) conducted by the present authors are also presented.

18 citations


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