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Wilhelm, Matthieu

Nom
Wilhelm, Matthieu
Affiliation principale
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Identifiants
https://libra.unine.ch/handle/123456789/879

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  • 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
    Métadonnées seulement
    Quasi systematic sampling
    (2015-6-25)
    Wilhelm, Matthieu 
    ;
    Tillé, Yves 
    We present a family of sampling designs depending on a integer parameter r. Then, simple random sampling is a particular case of this sampling design, namely when r = 1 and the systematic sampling design is the limiting case when r tends to the infinity. For every r > 0, this sampling design has the important property to have first and second order densities which are tractable and positive. Thus, the Horvitz-Thompson estimator is unbiased and the estimator of the variance of the Horvitz-Thompson estimator is also unbiased. This family of sampling design can be used in finite population or on any finite interval of R.
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    Modelling binomial, Poisson and gamma observations spatially distributed over irregularly shaped domains
    (2013-12-15)
    Wilhelm, Matthieu 
    A novel method is introduced 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 semi-parametric setting. The proposed model exploits advanced numerical analysis techniques, and specifically makes use of the Finite Element Method, that provide a basis for piecewise polynomial surfaces.
  • 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.