Meshless methods: An overview and recent developments

T. Belytschko; Y. Krongauz; D. Organ; M. Fleming; P. Krysl

doi:10.1016/S0045-7825(96)01078-X

Meshless methods: An overview and recent developments

T. Belytschko^*, Y. Krongauz, D. Organ, M. Fleming, P. Krysl

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

3117 Scopus citations

Abstract

Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.

Original language	English (US)
Pages (from-to)	3-47
Number of pages	45
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	139
Issue number	1-4
DOIs	https://doi.org/10.1016/S0045-7825(96)01078-X
State	Published - Dec 1 1996

Funding

The support of the Office of Naval Research,t he Air ResearchO ffice is gratefully acknowledged.

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(96)01078-X

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title = "Meshless methods: An overview and recent developments",

abstract = "Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.",

author = "T. Belytschko and Y. Krongauz and D. Organ and M. Fleming and P. Krysl",

note = "Funding Information: The support of the Office of Naval Research,t he Air ResearchO ffice is gratefully acknowledged.",

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T2 - An overview and recent developments

AU - Belytschko, T.

AU - Krongauz, Y.

AU - Organ, D.

AU - Fleming, M.

AU - Krysl, P.

N1 - Funding Information: The support of the Office of Naval Research,t he Air ResearchO ffice is gratefully acknowledged.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.

AB - Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined. It is shown that the three methods are in most cases identical except for the important fact that partitions of unity enable p-adaptivity to be achieved. Methods for constructing discontinuous approximations and approximations with discontinuous derivatives are also described. Next, several issues in implementation are reviewed: discretization (collocation and Galerkin), quadrature in Galerkin and fast ways of constructing consistent moving least-square approximations. The paper concludes with some sample calculations.

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JO - Computer Methods in Applied Mechanics and Engineering

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Meshless methods: An overview and recent developments

Abstract

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