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Stephen D. Bond

Citation:

Stephen D. Bond, Richard B. Lehoucq and Stephen T. Rowe, A Galerkin radial basis function method for nonlocal diffusion, In "Meshfree Methods for Partial Differential Equations VII", Lecture Notes in Computational Science and Engineering 100 (2014) 1-21.

Abstract:

We introduce a meshfree Galerkin method for solving nonlocal diffusion problems. Radial basis functions are used to construct an approximation scheme that requires only scattered nodes with no triangulation. A quadrature scheme specific to radial basis functions is implemented to produce a Galerkin radial basis function method that yields fast assembly of a sparse stiffness matrix. We provide numerical evidence for convergence rates using one and two dimensional nonlocal problems.

Full Text:

DOI: 10.1007/978-3-319-06898-5_1

Bibtex:
@article{BLR2014,
  author  = {Stephen D. Bond and Richard B. Lehoucq and Stephen T. Rowe},
  title   = {A Galerkin radial basis function method for nonlocal diffusion},
  journal = {Lecture Notes in Computational Science and Engineering},
  booktitle = {Meshfree Methods for Partial Differential Equations VII},
  volume  = 100,
  year    = 2014,
  pages   = {1--21},
  doi     = {10.1007/978-3-319-06898-5_1},
  note    = {SAND Number 2013-10673P}
}

Stephen Bond