Galerkin Meshless Methods Based on Partition of Unity Quadrature
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摘要: 数值积分是伽辽金无网格方法实施的一个重要环节，提出了一种适合于伽辽金无网格方法的单位分解积分技术．该积分技术建立在有限覆盖和单位分解基础之上，不需要对积分区域进行分解，具有较高的积分精度．并以无单元伽辽金方法为例，详细说明了基于单位分解积分的伽辽金无网格方法的实现过程．这样，在近似函数建立和数值积分过程中都不需要进行网格划分，从而形成一种“真正的”无网格方法．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.
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Key words:
- Galerkin meshless method /
- finite cover /
- partition of unity /
- numerical quadrature
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[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. -
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