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Numerical identification of a coefficient in a parabolic quasilinear equation

Jan Neumann (1985)

Aplikace matematiky

In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

Numerical procedure to approximate a singular optimal control problem

Silvia C. Di Marco, Roberto L.V. González (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we deal with the numerical solution of a Hamilton-Jacobi-Bellman (HJB) equation with infinitely many solutions. To compute the maximal solution – the optimal cost of the original optimal control problem – we present a complete discrete method based on the use of some finite elements and penalization techniques.

Numerical realization of a fictitious domain approach used in shape optimization. Part I: Distributed controls

Jana Daňková, Jaroslav Haslinger (1996)

Applications of Mathematics

We deal with practical aspects of an approach to the numerical realization of optimal shape design problems, which is based on a combination of the fictitious domain method with the optimal control approach. Introducing a new control variable in the right-hand side of the state problem, the original problem is transformed into a new one, where all the calculations are performed on a fixed domain. Some model examples are presented.

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2003)

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

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical resolution of an “unbalanced” mass transport problem

Jean-David Benamou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce a modification of the Monge–Kantorovitch problem of exponent 2 which accommodates non balanced initial and final densities. The augmented Lagrangian numerical method introduced in [6] is adapted to this “unbalanced” problem. We illustrate the usability of this method on an idealized error estimation problem in meteorology.

Numerical simulations for nodal domains and spectral minimal partitions

Virginie Bonnaillie-Noël, Bernard Helffer, Gregory Vial (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We recall here some theoretical results of Helffer et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire (2007) doi:10.1016/j.anihpc.2007.07.004] about minimal partitions and propose numerical computations to check some of their published or unpublished conjectures and exhibit new ones.

Numerical solution of the pressing devices shape optimization problem in the glass industry

Petr Salač (2018)

Applications of Mathematics

In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered. The state problem...

Numerical study of a new global minimizer for the Mumford-Shah functional in R3

Benoît Merlet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In [Progress Math.233 (2005)], David suggested the existence of a new type of global minimizers for the Mumford-Shah functional in 𝐑 3 . The singular set of such a new minimizer belongs to a three parameters family of sets ( 0 < δ 1 , δ 2 , δ 3 < π ) . We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdomains of 𝐒 2 with three reentrant corners. The necessary conditions are...

Numerical study of discretizations of multistage stochastic programs

Petri Hilli, Teemu Pennanen (2008)

Kybernetika

This paper presents a numerical study of a deterministic discretization procedure for multistage stochastic programs where the underlying stochastic process has a continuous probability distribution. The discretization procedure is based on quasi-Monte Carlo techniques originally developed for numerical multivariate integration. The solutions of the discretized problems are evaluated by statistical bounds obtained from random sample average approximations and out-of-sample simulations. In the numerical...

Nuovi risultati sulla semicontinuità inferiore di certi funzionali integrali

Luigi Ambrosio (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Given an open subset Ω of ℝ n and a Borel function f : Ω × ℝ × ℝ n → [ 0 , + ∞ [ , conditions on f are given which assure the lower semicontinuity of the functional ∫ Ω f ⁢ ( x , u , D ⁢ u ) ⁢ d ⁢ x with respect to different topologies.

Nuovi teoremi sulle funzioni a variazione limitata

Diego Pallara (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Vengono presentate alcune connessioni tra gli spazi classici delle funzioni a variazione limitata ed altre classi di funzioni la cui variazione è opportunamente controllata, cioè le classi GBV introdotte da E. De Giorgi e L. Ambrosio, e le classi BBV, LBV, GBV* introdotte in questa Nota. Le dimostrazioni dei risultati enunciati, insieme con altri dettagli, appariranno in un successivo lavoro.

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