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We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of th ...
In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...
Implicit Ordinary or Partial Differential Equations have been widely studied in recent times, essentially from the existence of solutions point of view. One of the main issues is to select a meaningful solution among the infinitely many ones. The most cele ...
Recently, we have shown how a colored-noise Langevin equation can be used in the context of molecular dynamics as a tool to obtain dynamical trajectories whose properties are tailored to display desired sampling features. In the present paper, after having ...
Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We descr ...
A complete model for single neurons must reproduce correctly the firing of spikes and bursts. Yet it must remain simple enough to be tractable in large-scale simulations. We present a study of a simplified model of Layer V pyramidal cells of the cortex wit ...
The purpose of this thesis is the study, from the numerical simulation point of view, of the aluminum electrolysis process. Navier-Stokes equations for the computation of a two fluids flow with free interface are coupled with Maxwell equations describing t ...
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of accuracy without ...
The main topic of this thesis is the study of the non-linear stochastic wave equation in spatial dimension greater than 3 driven by spatially homogeneous Gaussian noise that is white in time. We are interested in questions of existence and uniqueness of so ...