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Progress on Meshless Methods pp 37–56Cite as

Localized Radial Basis Functions with Partition of Unity Properties

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 11))

In this paper we introduce a localization of radial basis function (RBF) under the general framework of partition of unity. A reproducing kernel that repro¬duces polynomials is used as the localizing function of RBF. It is shown that the proposed approach yields a similar convergence to that of the non localized RBF, while a better conditioned discrete system than that of the radial basis collocation method is achieved. Analyses of error and stability of the proposed method for solving boundary value problems are presented. Numerical examples are given to demonstrate the effectiveness of the proposed method.

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Califormia, Los Angeles, CA, 90095-1593, USA

    Jiun-Shyan Chen & Wei Hu

  2. Department of Mathematics, Tunghai University, Taichung 407, Taiwan, R.O.C.

    Hsin-Yun Hu

Authors
  1. Jiun-Shyan Chen
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  2. Wei Hu
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  3. Hsin-Yun Hu
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Corresponding author

Correspondence to Jiun-Shyan Chen .

Editor information

Editors and Affiliations

  1. Departamento de Engenharia Mecânica e Gestão Industrial, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, Porto, 4200-465, Portugal

    A. J. M. Ferreira

  2. University of California Davis, California, USA

    E. J. Kansa

  3. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA

    G. E. Fasshauer

  4. Instituto Superior Técnico, DECivil/ICIST, TU Lisbon, Portugal

    V. M. A. Leitão

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Chen, JS., Hu, W., Hu, HY. (2009). Localized Radial Basis Functions with Partition of Unity Properties. In: Ferreira, A.J.M., Kansa, E.J., Fasshauer, G.E., Leitão, V.M.A. (eds) Progress on Meshless Methods. Computational Methods in Applied Sciences, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8821-6_3

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  • DOI: https://doi.org/10.1007/978-1-4020-8821-6_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-8820-9

  • Online ISBN: 978-1-4020-8821-6

  • eBook Packages: EngineeringEngineering (R0)

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