A Scalable Meshless Formulation Based on RBF Hermitian Interpolation for 3D Nonlinear Heat Conduction Problems
David Stevens1, Henry Power1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111
Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations.
The Kirchhoff transformation… More >
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