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Some applications of optimal control theory of distributed systems

Alfredo Bermudez — 2002

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we present some applications of the J.-L. Lions’ optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

Some Applications of Optimal Control Theory of Distributed Systems

Alfredo Bermudez — 2010

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we present some applications of the J.-L. Lions' optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

Finite element analysis of sloshing and hydroelastic vibrations under gravity

Alfredo BermúdezRodolfo Rodríguez — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with a finite element method to solve fluid-structure interaction problems. More precisely it concerns the numerical computation of harmonic hydroelastic vibrations under gravity. It is based on a displacement formulation for both the fluid and the solid. Gravity effects are included on the free surface of the fluid as well as on the liquid-solid interface. The pressure of the fluid is used as a variable for the theoretical analysis leading to a well posed mixed linear eigenvalue...

A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails

Alfredo BermúdezRodolfo RodríguezMaría Luisa Seoane — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the mathematical and numerical analysis of a simplified two-dimensional model for the interaction between the wind and a sail. The wind is modeled as a steady irrotational plane flow past the sail, satisfying the Kutta-Joukowski condition. This condition guarantees that the flow is not singular at the trailing edge of the sail. Although for the present analysis the position of the sail is taken as data, the final aim of this research is to develop tools to compute the sail...

A modal synthesis method for the elastoacoustic vibration problem

Alfredo BermúdezLuis Hervella-NietoRodolfo Rodríguez — 2002

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

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved, error...

An eddy current problem in terms of a time-primitive of the electric field with non-local source conditions

Alfredo BermúdezBibiana López-RodríguezRodolfo RodríguezPilar Salgado — 2013

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

The aim of this paper is to analyze a formulation of the eddy current problem in terms of a time-primitive of the electric field in a bounded domain with input current intensities or voltage drops as source data. To this end, we introduce a Lagrange multiplier to impose the divergence-free condition in the dielectric domain. Thus, we obtain a time-dependent weak mixed formulation leading to a degenerate parabolic problem which we prove is well-posed. We propose a finite element method for space...

A modal synthesis method for the elastoacoustic vibration problem

Alfredo BermúdezLuis Hervella-NietoRodolfo Rodríguez — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with Lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved,...

A fictitious domain method for the numerical two-dimensional simulation of potential flows past sails

Alfredo BermúdezRodolfo RodríguezMaría Luisa Seoane — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

This paper deals with the mathematical and numerical analysis of a simplified two-dimensional model for the interaction between the wind and a sail. The wind is modeled as a steady irrotational plane flow past the sail, satisfying the Kutta-Joukowski condition. This condition guarantees that the flow is not singular at the trailing edge of the sail. Although for the present analysis the position of the sail is taken as data, the final aim of this research is to develop tools to compute the sail...

Application of the optimal control theory to the wastewater elimination problem.

The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained optimal control...

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