The Mathematical Institute, University of Oxford, Eprints Archive

The Orthogonal Gradients Method: a Radial Basis Functions Method for Solving Partial Differential Equations on Arbitrary Surfaces

Piret, C. (2012) The Orthogonal Gradients Method: a Radial Basis Functions Method for Solving Partial Differential Equations on Arbitrary Surfaces. Journal of Computational Physics .

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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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1542
Deposited By:Peter Hudston
Deposited On:04 Jul 2012 09:05
Last Modified:04 Jul 2012 09:05

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