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In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...
Transformation invariance is an important property in pattern recognition, where different observations of the same object typically receive the same label. This paper focuses on a transformation invariant distance measure that represents the minimum dista ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
The modeling of a system composed by a gas phase and organic aerosol particles, and its numerical resolution are studied. The gas-aerosol system is modeled by ordinary differential equations coupled with a mixed-constrained optimization problem. This coupl ...
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight i ...
The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of sig ...
A novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated ...
Ordinary differential equations are coupled with mixed constrained optimization problems when modeling the thermodynamic equilibrium of a system evolving with time. A particular application arises in the modeling of atmospheric particles. Discontinuity poi ...
