IGS: An IsoGeometric approach for smoothing on surfaces

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• 作者：Matthieu Wilhelm^a ; ¹ ; ^{matthieu.wilhelm@unine.ch" class="auth_mail" title="E-mail the corresponding author} ; Luca Dedè ; ^b ; ² ; Laura M. Sangalli^c ; ³ ; Pierre Wilhelm^d ; ⁴
• 关键词：Functional data analysis ; Isogeometric analysis ; Smoothing on surfaces
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：70-89
• 全文大小：2401 K

文摘

We propose a novel approach for smoothing on surfaces. More precisely, we aim at estimating functions lying on a surface, starting from noisy and discrete measurements. The surface is 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 solving 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 16000025&_mathId=si2.gif&_user=111111111&_pii=S0045782516000025&_rdoc=1&_issn=00457825&md5=cd35b14d856e026ab3dc4847774f595e" title="Click to view the MathML source">C¹$C^1$-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.