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Kernel Radial Basis Functions

In: Computational Mechanics

Author

Listed:
  • W. Chen

    (Hohai University, Department of Engineering Mechanics)

  • H. Wang

    (Tianjin University, Department of Mechanics)

  • Q. H. Qin

    (Tianjin University, Department of Mechanics)

Abstract

This paper introduces new kernel radial basis functions (RBFs) which characterize partial differential equation problems of interest. Then we developed the meshfree collocation methods based on these kernel RBFs to solve benchmark Helmholtz, modified Helmholtz, and convection-diffusion problems. In comparison with the conventional RBFs such as multiquadratic (MQ), Gaussian, and thin plane spline, our preliminary numerical experiments show that the kernel RBFs perform pretty well in terms of accuracy, applicability, convergence, stability, and sensitivity to parameters. It is stressed that although the MQ has been widely popular for various problems of different types, it is also considered the kernel RBF of potential problem, and is not the RBF of choice for every problem. This study also presents some opening issues in the construction of the kernel RBF.

Suggested Citation

  • W. Chen & H. Wang & Q. H. Qin, 2007. "Kernel Radial Basis Functions," Springer Books, in: Computational Mechanics, pages 347-347, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75999-7_147
    DOI: 10.1007/978-3-540-75999-7_147
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