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Testing the method of multiple scales and the averaging principle for model parameter estimation of quasiperiodic two time-scale models

Papáček, Štěpán, Matonoha, Ctirad (2023)

Programs and Algorithms of Numerical Mathematics

Some dynamical systems are characterized by more than one time-scale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of...

The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2013)

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

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need the fundamental solution of the problem; furthermore...

The extended adjoint method

Stanislas Larnier, Mohamed Masmoudi (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Searching for the optimal partitioning of a domain leads to the use of the adjoint method in topological asymptotic expansions to know the influence of a domain perturbation on a cost function. Our approach works by restricting to local subproblems containing the perturbation and outperforms the adjoint method by providing approximations of higher order. It is a universal tool, easily adapted to different kinds of real problems and does not need...

The Lazy Travelling Salesman Problem in ℝ 2

Paz Polak, Gershon Wolansky (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study a parameter (σ) dependent relaxation of the Travelling Salesman Problem on  ℝ 2 . The relaxed problem is reduced to the Travelling Salesman Problem as σ → 0. For increasing σ it is also an ordered clustering algorithm for a set of points in ℝ 2 . A dual formulation is introduced, which reduces the problem to a convex optimization, provided the minimizer is in the domain of convexity of the relaxed functional. It is shown that this last condition is generically satisfied, provided σ is large enough. ...

The Mortar finite element method for Bingham fluids

Patrick Hild (2001)

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

This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.

The mortar finite element method for Bingham fluids

Patrick Hild (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the flow problem of a viscous plastic fluid in a cylindrical pipe. In order to approximate this problem governed by a variational inequality, we apply the nonconforming mortar finite element method. By using appropriate techniques, we are able to prove the convergence of the method and to obtain the same convergence rate as in the conforming case.

The optimization of heat radiation intensity

Mlýnek, Jaroslav, Srb, Radek (2013)

Programs and Algorithms of Numerical Mathematics

This article focuses on the problem of calculating the intensity of heat radiation and its optimization across the surface of an aluminium or nickel mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. In this way artificial leathers are produced in the car industry (e.g., the artificial leather on a car dashboard). The article includes a description of how a mathematical model allows us to calculate the...

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2004)

ESAIM: Control, Optimisation and Calculus of Variations

The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

The problem of data assimilation for soil water movement

François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.

The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...

The smooth continuation method in optimal control with an application to quantum systems

Bernard Bonnard, Nataliya Shcherbakova, Dominique Sugny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The motivation of this article is double. First of all we provide a geometrical framework to the application of the smooth continuation method in optimal control, where the concept of conjugate points is related to the convergence of the method. In particular, it can be applied to the analysis of the global optimality properties of the geodesic flows of a family of Riemannian metrics. Secondly, this study is used to complete the analysis of two-level dissipative quantum systems, where the system...

Three tabu search methods for the MI-FAP applied to 802.11 networks

Sacha Varone, Nicolas Zufferey (2008)

RAIRO - Operations Research - Recherche Opérationnelle

Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this...

Three tabu search methods for the MI-FAP applied to 802.11 networks

Sacha Varone, Nicolas Zufferey (2009)

RAIRO - Operations Research

Wireless LAN using IEEE 802.11 networks are now widely deployed at home by residential users or in hot spots by telecommunication operators. A hot spot is a place where a set of access points (APs) are located nearby each other and can serve many users. Since perturbations can degrade the quality of the signal, a careful channel assignment to each AP has to be done. Channel assignment of APs at hot spots, and more generally setup configuration and management, is still often done manually. In this...

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