Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2006)
Open Mathematics
Similarity:
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2005)
Open Mathematics
Similarity:
The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.
Othmar Koch, Christian Lubich (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial...
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...
Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We study a free energy computation procedure, introduced in [Darve and Pohorille, (2001) 9169–9183; Hénin and Chipot, (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre , (2008)...
Barkatou, Mohammed (2007)
Applied Mathematics E-Notes [electronic only]
Similarity: