About stability of equilibrium shapes
Marc Dambrine, Michel Pierre (2000)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
Displaying similar documents to “On variations of the shape Hessian and sufficient conditions for the stability of critical shapes.”
About stability of equilibrium shapes
On the ersatz material approximation in level-set methods
Marc Dambrine, Djalil Kateb (2010)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...
About stability of equilibrium shapes
Marc Dambrine, Michel Pierre (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We discuss the stability of "critical" or "equilibrium" shapes of a shape-dependent energy functional. We analyze a problem arising when looking at the positivity of the second derivative in order to prove that a critical shape is an optimal shape. Indeed, often when positivity -or coercivity- holds, it does for a weaker norm than the norm for which the functional is twice differentiable and local optimality cannot be deduced. We solve this problem for a particular but significant...
On stability analysis in shape optimization: critical shapes for Neumann poblem
M. Dambrine, J. Sokołowski, A. Żochowski (2003)
Control and Cybernetics
Similarity:
Critical points and nonlinear variational problems
Antonio Ambrosetti (1992)
Mémoires de la Société Mathématique de France
Similarity:
Approximation of a solidification problem
Rajae Aboulaïch, Ilham Haggouch, Ali Souissi (2001)
International Journal of Applied Mathematics and Computer Science
Similarity:
A two-dimensional Stefan problem is usually introduced as a model of solidification, melting or sublimation phenomena. The two-phase Stefan problem has been studied as a direct problem, where the free boundary separating the two regions is eliminated using a variational inequality (Baiocchi, 1977; Baiocchi et al., 1973; Rodrigues, 1980; Saguez, 1980; Srunk and Friedman, 1994), the enthalpy function (Ciavaldini, 1972; Lions, 1969; Nochetto et al., 1991; Saguez, 1980), or a control problem...