IGS: an IsoGeometric approach for Smoothing on surfaces

Matthieu Wilhelm, Luca Dedè, Laura M. Sangalli & Pierre Wilhelm

Abstract We propose an Isogeometric approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical representations commonly used in industrial applications. The estimation is based on the minimization of a penalized least-square functional. The latter is equivalent to solve a 4th-order Partial Differential Equation (PDE). In this context, we use Isogeometric Analysis (IGA) for the numerical approximation of such surface PDE, leading to an IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a surface. Indeed, IGA facilitates encapsulating the exact geometrical representation of the surface in the analysis and also allows the use of at least globally C^1-Continuous NURBS basis functions for which the 4th-order PDE can be solved using the standard Galerkin method. We show the performance of the proposed IGS method by means of numerical simulations and we apply it to the estimation of the pressure coefficient, and associated aerodynamic force on a winglet of the SOAR space shuttle.
Keywords Functional data analysis
Isogeometric analysis
Smoothing on surfaces
Citation Wilhelm, M., Dedè, L., Sangalli, L. M., & Wilhelm, P. (2016). IGS: an IsoGeometric approach for Smoothing on surfaces. Computer methods in applied mechanics and engineering, 302, 70-89.
Type Journal article (English)
Date of appearance 14-1-2016
Journal Computer methods in applied mechanics and engineering
Volume 302
Pages 70-89
URL http://ac.els-cdn.com/S0045782516000025/1-s2.0-S004578251...