Multivariate interpolation for fluid-structure-interaction problems using radial basis functions

By Armin Beckert, Holger Wendland. 2001

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Unified fluid–structure interpolation and mesh motion using radial basis functions (2008, methodology): “For p(x), Beckert and Wendland [48] used up to linear polynomials so that translation and rotation are recovered, i.e. if the wing simply translates or rotates then the interpolation at the fluid–structure interface does not change.”
Review of coupling methods for non-matching meshes (2007, methodology): “It would be very useful to vary the radius from center to center, but according to [8] theory only guarantees solvability for a ‘fixed’ radius.”
CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation (2008, methodology): “Although RBFs have been used for mesh deformation techniques in shape optimization [49] and structural–aerodynamic coupling [38, 50], their use in the current research is not to strictly or uniquely parameterize an aerodynamic shape, but to allow that initial shape and its corresponding aerodynamic ”
Kernel techniques: From machine learning to meshless methods (2006, methodology): “This has been done successfully, for example, in a series of papers (Farhat and Lesoinne 1998, Beckert 2000, Beckert and Wendland 2001, Ahrem, Beckert and Wendland 2005) and is already on its way to become an industry standard.”