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Galerkin meshless methods based on partition of unity quadrature

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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 is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses 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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Authors and Affiliations

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

    Zeng Qing-hong & Lu De-tang (Professor)

Authors
  1. Zeng Qing-hong
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  2. Lu De-tang
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Correspondence to Lu De-tang.

Additional information

Communicated by CHENG Geng-dong

Project supported by the National Natural Science Foundation of China (No. 10102020) and the National Basic Research Program of China (973 Project) (No. G1999032805)

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Qing-hong, Z., De-tang, L. Galerkin meshless methods based on partition of unity quadrature. Appl Math Mech 26, 893–899 (2005). https://doi.org/10.1007/BF02464238

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  • DOI: https://doi.org/10.1007/BF02464238

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Chinese Library Classification

2000 Mathematics Subject Classification

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