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An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab
An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab
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In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …