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Central WENO schemes for hyperbolic systems of conservation laws

Doron Levy, Gabriella Puppo, Giovanni Russo (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a family of high-order, essentially non-oscillatory, central schemes for approximating solutions of hyperbolic systems of conservation laws. These schemes are based on a new centered version of the Weighed Essentially Non-Oscillatory (WENO) reconstruction of point-values from cell-averages, which is then followed by an accurate approximation of the fluxes via a natural continuous extension of Runge-Kutta solvers. We explicitly construct the third and fourth-order scheme and demonstrate...

Central-upwind schemes for the Saint-Venant system

Alexander Kurganov, Doron Levy (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central schemes...

Central-Upwind Schemes for the Saint-Venant System

Alexander Kurganov, Doron Levy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present one- and two-dimensional central-upwind schemes for approximating solutions of the Saint-Venant system with source terms due to bottom topography. The Saint-Venant system has steady-state solutions in which nonzero flux gradients are exactly balanced by the source terms. It is a challenging problem to preserve this delicate balance with numerical schemes. Small perturbations of these states are also very difficult to compute. Our approach is based on extending semi-discrete central...

Certified metamodels for sensitivity indices estimation

Alexandre Janon, Maëlle Nodet, Clémentine Prieur (2012)

ESAIM: Proceedings

Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much faster to run. In this case, estimated indices are subject to two kinds of errors: sampling error, caused...

Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values

Alexandre Janon, Maëlle Nodet, Clémentine Prieur (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.

Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Jakub Kůdela, Pavel Popela (2018)

Kybernetika

In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....

Change-point estimation from indirect observations. 2. Adaptation

A. Goldenshluger, A. Juditsky, A. Tsybakov, A. Zeevi (2008)

Annales de l'I.H.P. Probabilités et statistiques

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable practical...

Chaos synchronization of TSUCS unified chaotic system, a modified function projective control method

Hamed Tirandaz (2018)

Kybernetika

The synchronization problem of the three-scroll unified chaotic system (TSUCS) is studied in this paper. A modified function projective synchronization (MFPS) method is developed to achieve this goal. Furthermore, the only parameter of the TSUCS unified chaotic system is considered unknown and estimated with an appropriate parameter estimation law. MFPS method is investigated for both identical and non-identical chaotic systems. Lyapunov stability theorem is utilized to verify the proposed feedback...

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