Solving differential equations with radial basis functions: multilevel methods and smoothing

@article{Fasshauer1999SolvingDE,
  title={Solving differential equations with radial basis functions: multilevel methods and smoothing},
  author={Gregory E. Fasshauer},
  journal={Adv. Comput. Math.},
  year={1999},
  volume={11},
  pages={139-159}
}
Some of the meshless radial basis function methods used for the numerical solution of partial diierential equations are reviewed. In particular, the diierences between globally and locally supported methods are discussed, and for locally supported methods the important role of smoothing within a multilevel framework is demonstrated. A possible connection between multigrid nite elements and multilevel radial basis function methods with smoothing is explored. Various numerical examples are also… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 46 references

Numerical solution of variational problems by radial basis func tions, in Approximation Theory

  • H. Wendland
  • 1998
Highly Influential
20 Excerpts

The Laplace transform multiquadric method: A highly accurate scheme for the numerical solution of linear partial di erential equations

  • G. J. Moridis, E. J. Kansa
  • J. Appl. Sci. Comp
  • 1994
Highly Influential
7 Excerpts

Approximate solution of systems of linear equations (originally published as: Angen aherte Au osung von Systemen linearer Gleichungen

  • S. Kaczmarz
  • Bul letin International de l'Academie Polonaise…
  • 1993
Highly Influential
6 Excerpts

Moving node methods for PDE's using radial basis functions and B-splines

  • D. Djokovi c, R. van Damme
  • 1997
Highly Influential
6 Excerpts

Radial splines and moving grids, preprint

  • D. Djokovi c, R. van Damme
  • 1996
Highly Influential
6 Excerpts

An adaptive Newton algorithm based on numerical inversion: regularization as postconditioner

  • J. W. Jerome
  • Numer. Math
  • 1985
Highly Influential
4 Excerpts

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