Galerkin Meshless Methods Based on Partition of Unity Quadrature

ZENG Qing-hong; LU De-tang

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ZENG Qing-hong, LU De-tang. Galerkin Meshless Methods Based on Partition of Unity Quadrature[J]. Applied Mathematics and Mechanics, 2005, 26(7): 819-825.

Citation:

ZENG Qing-hong, LU De-tang. Galerkin Meshless Methods Based on Partition of Unity Quadrature[J]. Applied Mathematics and Mechanics, 2005, 26(7): 819-825.

Citation:

ZENG Qing-hong, LU De-tang. Galerkin Meshless Methods Based on Partition of Unity Quadrature[J]. Applied Mathematics and Mechanics, 2005, 26(7): 819-825.

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Galerkin Meshless Methods Based on Partition of Unity Quadrature

Department of Mechanics and Mechanic Engineering, University of Science and Technology of China, Hefei 230027, P. R. China

Received Date: 2003-07-07
Rev Recd Date: 2005-03-15
Publish Date: 2005-07-15

Abstract

Abstract

Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature (PUQ), for Galerkin meshless methods was presented. The technique was based on finite covering and partition of unity. There was no need to decompose the physical domain into small cell. If possessed remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are "truly" meshless methods.
- Galerkin meshless method,
- finite cover,
- partition of unity,
- numerical quadrature

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References(9)

References

[1]	Belytschko T,Lu Y Y,Gu L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2):229—256. doi: 10.1002/nme.1620370205
[2]	Lu Y Y,Belytschko T,Gu L.A new implementation of the element free Galerkin method[J].Computer Methods in Applied Mechanics and Engineering,1994,113(3/4):397—414. doi: 10.1016/0045-7825(94)90056-6
[3]	Beissel S,Belytschko T.Nodal integration of the element-free Galerkin method[J].Computer Methods in Applied Mechanics and Engineering,1996,139(1/4):49—74. doi: 10.1016/S0045-7825(96)01079-1
[4]	Chen J S,Wu C T,Yoon S,et al.A stabilized conforming nodal integration for Galerkin mesh-free methods[J].International Journal for Numerical Methods in Engineering,2001,50(2):435—466. doi: 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
[5]	Dolbow J,Belytschko T.Numerical integration of the Galerkin weak form in meshfree methods[J].Computational Mechanics,1999,23(3):219—230. doi: 10.1007/s004660050403
[6]	Belytschko T, Krongauz Y,Organ D,et al.Meshless methods: an overview and recent developments[J].Computer Methods in Applied Mechanics and Engineering,1996,139(1/4):3—47. doi: 10.1016/S0045-7825(96)01078-X
[7]	Marc D,Hung N D.A truly meshless Galerkin method based on a moving least squares quadrature[J].Communications in Numerical Methods in Engineering,2002,18(1):1—9.
[8]	Liszka T J,Duarte C A M,Tworzydlo W W.Hp-meshless cloud method[J].Computer Methods in Applied Mechanics and Engineering,1996,139(1/4):263—288. doi: 10.1016/S0045-7825(96)01086-9
[9]	刘欣,朱德懋,陆明万,等.基于流行覆盖思想德无网格方法的研究[J].计算力学学报,2001,18(1):21—27.