Environmental models often involve complex dynamic and spatial inputs and outputs. This raises specific issues when performing uncertainty and sensitivity analyses (SA). Based on applications in flood risk assessment and agro-ecology, we present current research to adapt the methods of variance-based SA to such models. After recalling the basic principles, we propose a...
This article presents several state-of-the-art Monte Carlo methods for simulating and estimating rare events. A rare event occurs with a very small probability, but its occurrence is important enough to justify an accurate study. Rare event simulation calls for specific techniques to speed up standard Monte Carlo sampling, which requires unacceptably large sample sizes to observe...
Wind power is an intermittent resource due to wind speed intermittency. However wind speed can be described as a stochastic process with short memory. This allows us to derive a central limit theorem for the annual or pluri-annual wind power production and then get quantiles of the wind power production for one, ten or twenty years future periods. On the one hand, the...
In this survey we present an analytic approach to solve problems concerning (deterministic or random) walks in the quarter plane. We illustrate the recent breakthroughs in that domain with two examples. The first one is about the combinatorics of walks confined to the quarter plane, and more precisely about the numbers of walks evolving in the quarter plane and having given...
Random laminations of the disk are the continuous limits of random non-crossing configurations of regular polygons. We provide an expository account on this subject. Initiated by the work of Aldous on the Brownian triangulation, this field now possesses many characters such as the random recursive triangulation, the stable laminations and the Markovian hyperbolic triangulation of...
Interacting particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics and information engineering. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their...
This paper deals with the representation of the trace of iterative Schwarz solutions at the interfaces of domain decomposition to approximate adaptively the interface error operator. This allows to build a cost-effectively accelerating of the convergence of the iterative method by extending to the vectorial case the Aitken’s accelerating convergence technique. The first...
This paper adresses the approximation of the dynamic impact of thin elastic structures. The principle of the presented method is the use of a singular mass matrix obtained by different discretizations of the deflection and velocity. The obtained semi-discretized problem is proved to be well-posed and energy conserving. The method is applied on some membrane, beam and plate models...
Gyrokinetic simulations lead to huge computational needs. Up to now, the semi- Lagrangian code Gysela performed large simulations using a few thousands cores (8k cores typically). Simulation with finer resolutions and with kinetic electrons are expected to increase those needs by a huge factor, providing a good example of applications requiring Exascale machines. This paper...
We propose in this article to compare the efficiency of two chemotherapeutic schedules: the traditional and the metronomic. For this, we develop a new mathematical model describing the growth dynamics of tumor and endothelial cells as well as the impact of molecules as oxygen or vascular endothelial growth factor on this dynamics. The model construction: biological assumptions...
This article deals with the problem of computing numerical approximations of null-controls for parabolic equations or systems by using the Hilbert Uniqueness Method (HUM). We mainly review recent results on this subject but we also provide new elements to emphasize the main ideas underlying the penalised HUM approach which is at the heart of the methods used in practice. We give...
The parallelization performance of the TERESA Code for Trapped Element REduction in Semi lagrangian Approach is analyzed. TERESA is a kinetic code in four dimensions (4D), two in "real
In this paper we present applications of the reduced basis method (RBM) to large-scale non-linear multi-physics problems. We first describe the mathematical framework in place and in particular the Empirical Interpolation Method (EIM) to recover an affine decomposition and then we propose an implementation using the open-source library Feel++ which provides both the reduced basis...
This paper addresses the numerical approximation of uid dynamics problems using various finite element methods including high order methods and high order geometry. The paper is divided in three parts. The first part concerns the various problem formulations and discretization methods we are interested in. Using the Stokes equations as model, several different types of boundary...
We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via Harten’s cell average multiresolution analysis, which...
In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF2D (http ://www.univ-orleans.fr/mapmo/soft/FullSWOF/ that solves shallow water equations for applications in hydrology) based on a domain decomposition strategy. The first approach is based on the classical MPI library while the second approach uses Parallel...
We review in this paper an explicit scheme for the numerical simulation of inviscid compressible flows; we analyze it for both the barotropic Euler equations and the full Euler equations for an ideal gas. In each case, we summarize the theoretical results that were recently obtained concerning the stability and consistency of the schemes and present some numerical results which...
The problem of drop formation and pinch-off from a capillary tube under the influence of gravity has been extensively studied when the internal capillary pressure gradient is constant. This ensures a continuous time independent flow field inside the capillary tube typically of the Poiseuille flow type. Characteristic drop ejection behaviour includes: periodic drop ejection, drop...
We present several numerical simulations of conservation laws on recent multicore processors, such as GPUs, using the OpenCL programming framework. Depending on the chosen numerical method, different implementation strategies have to be considered, for achieving the best performance. We explain how to program efficiently three methods: a finite volume approach on a structured...
We discuss recent results on chaos synchronization of delayed systems. We investigate the limit of large coupling delays and discuss how in this limit the stability problem for the synchronized solution is drastically simplified. We use these results to derive rigorous conditions for chaos synchronization of all-optically coupled laser networks. In laser systems the optical...
The propagation of traveling waves in excitable media with randomly distributed diffusion coefficient is studied. If the characteristic size of the waves is much larger than the heterogeneity size an effective medium theory based on a self-consistent homogenization approach can be applied. The random distribution of the medium properties is produced by domains of two phases. In...