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Wilhelm, Matthieu

Nom
Wilhelm, Matthieu
Affiliation principale
Fonction
Ancien.ne collaborateur.trice
Identifiants
https://libra.unine.ch/handle/123456789/879

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  • Publication
    Métadonnées seulement
    Generalized Spatial Regression with Differential Regularization
    (2016-5-10)
    Wilhelm, Matthieu 
    ;
    Sangalli, Laura M.
    We propose a method for the analysis of data scattered over a spatial irregularly shaped domain and having a distribution within the exponential family. This is a generalized additive model for spatially distributed data. The model is fitted by maximizing a penalized log-likelihood function with a roughness penalty term that involves a differential operator of the spatial field over the domain of interest. Efficient spatial field estimation is achieved resorting to the finite element method, which provides a basis for piecewise polynomial surfaces. The method is illustrated by an application to the study of criminality in the city of Portland, Oregon, USA.
  • Publication
    Métadonnées seulement
    IGS: an IsoGeometric approach for Smoothing on surfaces
    (2016-1-14)
    Wilhelm, Matthieu 
    ;
    Dedè, Luca
    ;
    Sangalli, Laura M.
    ;
    Wilhelm, Pierre
    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.
  • Publication
    Métadonnées seulement
    IsoGeometric Smoothing: A new approach for smoothing on surfaces
    (2015-12-12)
    Wilhelm, Matthieu 
    ;
    Dedè, Luca
    ;
    Sangalli, Laura M.
    ;
    Wilhelm, Pierre
    We propose a new approach for smoothing on surfaces. 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 which is equivalent to solve a 4th-order Partial Differential Equation (PDE). We use Isogeometric Analysis (IGA), which is a method for numerically solve PDE, for the numerical approximation of such surface PDE, leading to an IsoGeometric Smoothing (IGS) method. IGA has the great advantage to use the exact geometrical representation of the surface in the analysis, thus avoiding complex meshing procedures. IGA also provides at least globally $C^1-$continuous basis functions with compact support. 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.
  • Publication
    Accès libre
    Generalized Spatial Regression with Differential Penalization
    (2013-9-9)
    Wilhelm, Matthieu 
    ;
    Sangalli, Laura M.
    We introduce a novel method for the analysis of spatially distributed data from an exponential family distribution, able to efficiently deal with data occurring over irregularly shaped domains. The proposed generalized additive framework can handle all distributions within the exponential family, including binomial, Poisson and gamma outcomes, hence leading to a very broad applicability of the model. Specifically, we maximize a penalized log-likelihood function where the roughness penalty term involves a suitable differential operator of the spatial field over the domain of interest. Space-varying covariate information can also be included in the model in a semiparametric setting. The proposed model exploits advanced scientific computing techniques and specifically makes use of the Finite Element Method, that provide a basis for piecewise polynomial surfaces.