Journal ArticleDOI
A finite point method in computational mechanics. applications to convective transport and fluid flow
TLDR
In this article, the finite point method (FPM) is proposed for solving partial differential equations, which is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals.Abstract:
The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non-self adjoint equations typical of convective-diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.read more
Citations
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Journal ArticleDOI
Review: Meshless methods: A review and computer implementation aspects
TL;DR: This manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate the discourse.
Journal ArticleDOI
A point interpolation meshless method based on radial basis functions
Jianguo Wang,Gui-Rong Liu +1 more
TL;DR: In this article, a point interpolation meshless method is proposed based on combining radial and polynomial basis functions, which makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least-squares approximation.
Journal ArticleDOI
Meshfree and particle methods and their applications
Shaofan Li,Wing Kam Liu +1 more
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Journal ArticleDOI
A new class of accurate, mesh-free hydrodynamic simulation methods
TL;DR: In this paper, a Lagrangian method for hydrodynamics is proposed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes.
Journal ArticleDOI
The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods
Satya N. Atluri,Shengping Shen +1 more
TL;DR: In this paper, a comparison study of the efficiency and ac- curacy of a variety of meshless trial and test functions is presented, based on the general concept of the meshless local Petrov-Galerkin (MLPG) method.
References
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Journal ArticleDOI
Smoothed particle hydrodynamics: Theory and application to non-spherical stars
R. A. Gingold,Joseph J Monaghan +1 more
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
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Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
A. N. Brooks,Thomas J. R. Hughes +1 more
TL;DR: In this article, a new finite element formulation for convection dominated flows is developed, based on the streamline upwind concept, which provides an accurate multidimensional generalization of optimal one-dimensional upwind schemes.
Journal ArticleDOI
Reproducing kernel particle methods
TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).
Journal ArticleDOI
Generalizing the finite element method: Diffuse approximation and diffuse elements
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
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