# Advanced Field Data Post-processing Using RBF Interpolation

## Abstract

In this chapter a collection of application faced with an advanced post-processing method based on RBF fields is presented. The idea is that field information known at discrete points in a continuum domain (displacement field of an elastic body subjected to load and deformed, local speed and pressure in a fluid) can be interpolated so that scattered information becomes continuous and, in some cases, differentiable. Examples based on the theory of elasticity are firstly provided: the post-processing of a FEA solution available as a displacement field can be used to compute strains and stresses with the benefit to make them mesh independent (and so ready to be used for the generation of various plot) and better resolved in the space despite the coarseness of the field. Experimental data can be processed according to the same principle so that RBF become an useful tool for strain and stress evaluation by image processing. The chapter then addresses another useful application of RBF mapping suitable for the compensation of metrological data: a complex environment that loads the structure and can adversely affect the quality of the measurement can be subtracted by the inverse mapping of the displacement field achieved by FEA so that measured points can be corrected and positioned in their undeformed configuration for an effective comparison with reference CAD geometry. The chapter is concluded showing how RBF can be used for the interpolation of experimentally acquired flow information related to hemodynamics and showing the potential of an upscaling post processing toward the reduction of the resolution of in vivo acquired flow field (and so the exposition time of the patient).

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