Scattered node compact finite difference-type formulas generated from radial basis functions

In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered...

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Published in:Journal of computational physics 2006-02, Vol.212 (1), p.99-123
Main Authors: Wright, Grady B., Fornberg, Bengt
Format: Article
Language:English
Subjects:
Compact
Computational techniques
Exact sciences and technology
Finite difference method
Mathematical methods in physics
Mehrstellenverfahren
Mesh-free
Partial differential equations
Physics
Radial basis functions
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description In standard equispaced finite difference (FD) formulas, symmetries can make the order of accuracy relatively high compared to the number of nodes in the FD stencil. With scattered nodes, such symmetries are no longer available. The generalization of compact FD formulas that we propose for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil nodes small without a similar reduction in accuracy. We analyze the accuracy of these new compact RBF-FD formulas by applying them to some model problems, and study the effects of the shape parameter that arises in, for example, the multiquadric radial function.
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subjects Compact
Computational techniques
Exact sciences and technology
Finite difference method
Mathematical methods in physics
Mehrstellenverfahren
Mesh-free
Partial differential equations
Physics
Radial basis functions
title Scattered node compact finite difference-type formulas generated from radial basis functions
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