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Article
The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces
Journal of Computational Physics (2012)
  • Cecile M Piret
Abstract
Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time.
Keywords
  • Radial basis functions,
  • RBF,
  • Closest point method,
  • Implicit surfaces,
  • Level set method,
  • Orthogonal gradients method,
  • OGr method
Disciplines
Publication Date
May 20, 2012
DOI
10.1016/j.jcp.2012.03.007
Publisher Statement
© 2014 Journal of Computational Physics. Deposited in compliance with publisher policies. Publisher's version of record: http://www.sciencedirect.com/science/article/pii/S0021999112001477
Citation Information
Cecile M Piret. "The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces" Journal of Computational Physics Vol. 231 Iss. 14 (2012) p. 4662 - 4675
Available at: http://works.bepress.com/cecile_piret/6/