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Least‐squares collocation meshless method
International Journal for Numerical Methods in Engineering, 2001AbstractA finite point method, least‐squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satisfied not only at the collocation points but also at the ...
Zhang, Xiong +3 more
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SOLVING BURGERS EQUATION BY A MESHLESS METHOD
Modern Physics Letters B, 2005Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport.
Shi, B. J. +3 more
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Meshless method with ridge basis functions
Applied Mathematics and Computation, 2010The authors introduce a meshless method based on collocation with ridge basis functions. They briefly show the existence and uniqueness of the discrete solution and solve two elementary boundary value problems. The exact solutions are computed with modest accuracy.
Zhigang Wang +5 more
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Simulation of Impact and Fragmentation With the Meshless Methods
ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 4, 2010High velocity impact and penetration problems include large deformation, erosion, high strain rate dependent nonlinear material behavior and fragmentation. Therefore, meshless methods seem to be ideally suited for the modeling of penetration events as they allow unrestricted deformation and easy tracking of material interfaces and loading histories. In
Namık Kılıc¸ +2 more
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On Approximation in Meshless Methods
2005We analyze the approximation properties of some meshless methods. Three types of functions systems are discussed: systems of functions that reproduce polynomials, a class of radial basis functions, and functions that are adapted to a differential operator.
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The basis of meshless domain discretization: the meshless local Petrov?Galerkin (MLPG) method
Advances in Computational Mathematics, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Satya N. Atluri, Shengping Shen
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2014
In this chapter the most important meshless method concepts are detailed introduced. The chapter stars with a generic description on the meshless procedure. Additionally, it is presented a brief comparison between procedures of the finite element method (FEM) and the meshless method.
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In this chapter the most important meshless method concepts are detailed introduced. The chapter stars with a generic description on the meshless procedure. Additionally, it is presented a brief comparison between procedures of the finite element method (FEM) and the meshless method.
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Meshless RKHPU method and its applications
Mathematics and Computers in Simulation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2009
Preface Particular Solution of Poisson Problems using Cardinal Lagrangian Polyharmonic Splines, by B. Bacchelli and M. Bozzini A Meshless Solution to the p-Laplace Equation, by F. Bernal and M. Kindelan Localized Radial Basis Functions with Partition of Unity Properties, by J.S. Chen, W. Hu and H.Y.
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Preface Particular Solution of Poisson Problems using Cardinal Lagrangian Polyharmonic Splines, by B. Bacchelli and M. Bozzini A Meshless Solution to the p-Laplace Equation, by F. Bernal and M. Kindelan Localized Radial Basis Functions with Partition of Unity Properties, by J.S. Chen, W. Hu and H.Y.
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