Arnaud Münch

Optimal location of the support of the control for the 1-D wave equation: numerical investigations

Abstract We consider in this paper the homogeneous 1-D wave equation defined on Ω⊂ℝ. Using the Hilbert Uniqueness Method, one may define, for each subset ω⊂Ω, the exact control vω of minimal L2(ω×(0,T))-norm which drives to rest the system at a time T>0 large enough. We address the question of the optimal position of ω which minimizes the functional

Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation

J:\omega \rightarrow \|v_{\omega}\|_{L^{2}(\omega \times (0,T))}

Numerical null controllability of the heat equation through a least squares and variational approach

. We express the shape derivative of J as an integral on ∂ω×(0,T) independently of any adjoint solution. This expression leads to a descent direction for J and permits to define a gradient algorithm efficiently initialized by the topological derivative associated with J. The numerical approximation of the problem is discussed and numerical experiments are presented in the framework of the level set approach. We also investigate the well-posedness of the problem by considering a relaxed formulation.

Numerical simulation of delamination growth in curved interfaces

We consider a two-phase isotropic optimal design problem within the context of the transient heat equation. The objective is to minimize the average of the dissipated thermal energy during a fixed time interval

MATHEMATICAL ANALYSIS OF NONLINEAR BONDED JOINT MODELS

[0,T]

Numerical simulation of debonding of adhesively bonded joint

. The time-independent material properties are taken as design variables. A full relaxation for this problem was established in [A. Munch, P. Pedregal, and F. Periago, J. Math. Pures Appl. (9), 89 (2008), pp. 225-247] by using the homogenization method. In this paper, we study the asymptotic behavior as

Optimal design under the one-dimensional wave equation

T

Controllability of the Linear One-dimensional Wave Equation with Inner Moving Forces

goes to infinity of the solutions of the relaxed problem and prove that they converge to an optimal relaxed design of the corresponding two-phase optimization problem for the stationary heat equation. Next we study necessary optimality conditions for the relaxed optimization problem under the transient heat equation and use those to characterize the microstructure of the optimal designs, which appears in the form of a sequential laminate of rank at most

Numerical approximation of bang-bang controls for the heat equation: an optimal design approach

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Optimal Internal Dissipation of a Damped Wave Equation Using a Topological Approach

, the spatial dimension. An asymptotic analysis of the optimality conditions lets us prove that, for