Foreword to the special issue of Arima Journal dedicated to TAM-TAM'09

This paper aims at the development of innovating methods for optimum design for multidisciplinary optimization problems in the aeronautical context. The subject is the treatment of a problem of concurrent optimization in which the aerodynamicist interacts with the structural designer, in a parallel way in a symmetric Nash game. Algorithms for the calculation of the equilibrium point have been proposed and successfully tested for this coupled aero-structural shape optimization in a situation where the aerodynamical criterion is preponderant.

Using a preconditioned Richardson iterative method as a regularization to the data completion problem is the aim of the contribution. The problem is known to be exponentially ill posed that makes its numerical treatment a hard task. The approach we present relies on the Steklov-Poincaré variational framework introduced in [Inverse Problems, vol. 21, 2005]. The resulting algorithm turns out to be equivalent to the Kozlov-Maz’ya-Fomin method in [Comp. Math. Phys., vol. 31, 1991]. We conduct a comprehensive analysis on the suitable stopping rules that provides some optimal estimates under the General Source Condition on the exact solution. Some numerical examples are finally discussed to highlight the performances of the method.

The time-dependent Stokes equations are discretized by the original Chorin’s projection method [5] and Temam[15]. According to an idea of [1], we derive time error estimators for velocity and pressure. In particular, the velocity estimator is implemented for adaptation on the time step.

Haddar and Kress [9] extended the use of the conformal mapping approach [2, 8] to reconstruct the internal boundary curve Ti of a doubly connected domain from the Cauchy data on the external boundary of a harmonic function satisfying a homogeneous impedance boundary condition on Ti. However, the analysis of this scheme indicates non convergence of the proposed algorithm for small values of the impedance. In this paper, we modify the algorithm proposed in [9] in order to obtain a convergent and stable inversion process for small impedances. We illustrate the performance of the method through some numerical examples that also include the cases of variable impedances.

In a recent work Gratie has generalized the classical Marguerre-von Kármán equations studied by Ciarlet and Paumier in [2], where only a portion of the lateral face is subjected to boundary conditions of von Kármán’s type and the remaining portion being free. She shows that the leading term of the asymptotic expansion is characterized by a two-dimensional boundary value problem. In this paper, we extend formally this study to dynamic case.

We are interested here, in multi-criteria optimization problem using game theory. This problem will be treated by using a new algorithm for the splitting of territory in case of concurrent optimization, which presents a new formulation of Nash games between two players using two tables of allocations. Each player minimizes his cost function using the variables allocated by his own table. The two tables are given by an iterative algorithm. An image processing problem is addressed by using the proposed algorithms.

A new method for parallel beam tomography is proposed. This method is based on the topological gradient approach. The use of the topological asymptotic analysis for detecting the main edges of the data allows us to filter the noise while inverting the Radon transform. Experimental results obtained on noisy data illustrate the efficiency of this promising approach in the case of Magnetic Resonance Imaging. We also study the sensitivity of the algorithm with respect to several regularization and weight parameters.

The continued growth in demand for electricity is a increasingly challenge for the company. This requires great efforts to optimize decisions to be taken especially for managing the distribution of electricity which poses many problems in society, primarily due to the expansion of the network, increased consumption Power and real-time management. As the strengthening of electrical networks is difficult and expensive at the same time, it is necessary to choose an optimal management to ensure customer satisfaction, reduce costs and increase profit margins. In this work, we propose a few different optimization methods to solve partially or globally this problem, allowing to make appropriate choices.

This work consists to determine in a practical and straightforward manner some efficient sequential sampling schemes in order to estimate the product of Bernoulli parameters. The sampling schemes given by the literature are complex and costly. The results are useful for estimating the reliability of series/parallel systems where the allocation of the number of units to be tested from each component can be effective for minimizing the variance of the estimator.