Journal Article10.1016/J.APM.2018.06.040
Three-dimensional complex variable element-free Galerkin method
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TL;DR: Numerical results reveal that the CVEFG method has better accuracy and higher computational efficiency than other methods such as the element-free Galerkin method.
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About: This article is published in Applied Mathematical Modelling. The article was published on 01 Nov 2018. The article focuses on the topics: Galerkin method & Moving least squares.
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Citations
A truly meshfree method for solving acoustic problems using local weak form and radial basis functions
Xiangyu You,Wei Li,Yingbin Chai +2 more
TL;DR: The results of several numerical examples have shown that with same group of field nodes the present methodology can lead to much more accurate solutions than finite element approach, in particular for relatively high frequencies, and can also generate comparable solutions in comparison to other global Galerkin meshfree techniques.
69
Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions
TL;DR: This paper sets up a framework for the theoretical error analysis of the LMFS, and the fundamental solutions-based MLS approximation, named as an augmented MLS (AMLS) approximation, is generalized to any point in the computational domain.
62
A meshless singular boundary method for transient heat conduction problems in layered materials
Lin Qiu,Fajie Wang,Ji Lin +2 more
TL;DR: Numerical results clearly indicate the efficiency, accuracy and stability of the presented SBM for solving transient heat conduction problems in layered materials.
57
The interpolating element-free Galerkin method for three-dimensional elastoplasticity problems
Q. Wu,Fengbin Liu,Yumin Cheng +2 more
TL;DR: In this paper, the interpolating element-free Galerkin (IEFG) method for solving the 3D elastoplasticity problems is presented, which can apply the displacement boundary conditions directly, which results in higher computational efficiency and accuracy.
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Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions
TL;DR: This paper makes a first attempt to apply the localized method of fundamental solutions for analysis of 3D interior acoustic fields by first divides the whole computational domain into some overlapping subdomains, and then expresses physical variables as linear combinations of the fundamental solution in each subdomain.
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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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Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TL;DR: In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.
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Mesh Free Methods: Moving Beyond the Finite Element Method
Gui-Rong Liu
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TL;DR: In this paper, Galerkin et al. defined mesh-free methods for shape function construction, including the use of mesh-less local Petrov-Galerkin methods.
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H‐p clouds—an h‐p meshless method
TL;DR: The approximating properties of the h-p cloud functions are investigated in this article and a several theorems concerning these properties are presented.