Abstract. Structure and fluid models need to be combined, or coupled, when problems of fluidstructure interaction (FSI) are addressed. We first present the basic knowledge required for building and then evaluating a simple coupling. The approach proposed is to consider a dedicated solver for each of the two physical systems involved. We illustrate this approach by examining the interaction between a gas contained in a one-dimensional chamber closed by a moving piston attached to an external and fixed point with a spring. A single model is introduced for the structure, while three models of increasing complexity are proposed for the fluid flow solver. The most complex fluid flow model leads us to the arbitrary Lagrangian Eulerian (ALE) approach. The pros and cons of each model are discussed. The computer implementations of the structure model, the fluid model, and the coupling use MATLAB scripts, downloadable from either http://www.utc.fr/∼elefra02/ifs or http://www.hds.utc.fr/∼boufflet/ifs.

The aim of this article is to explore the possibility of using a family of fixed finite elements shape functions to solve a Dirichlet boundary value problem with an alternative variational formulation. The domain is embedded in a bounding box and the finite element approximation is associated to a regular structured mesh of the box. The shape of the domain is independent of the discretization mesh. In these conditions, a meshing tool is never required. This may be especially useful in the case of evolving domains, for example shape optimization or moving interfaces. This is not a new idea, but we analyze here a special approach. The main difficulty of the approach is that the associated quadratic form is not coercive and an inf-sup condition has to be checked. In dimension one, we prove that this formulation is well posed and we provide error estimates. Nevertheless, our proof relying on explicit computations is limited to that case and we give numerical evidence in dimension two that the formulation does not provide a reliable method. We first add a regularization through a Nitsche term and we observe that some instabilities still remain. We then introduce and justify a geometrical regularization. A reliable method is obtained using both regularizations.

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International audienceWe address the examination timetabling problem proposed in the second International Timetabling Competition (ITC2007). This paper presents newpreprocessing stages and an improved mixed integer mathematical model. An exam-based conflict graph in which edges represent incompatibilities between exams is used. The preprocessing stages make use of the graph, together with hard constraints and room capacities, to reveal implicit constraints. Results show that the new preprocessing stages increase up to 106 % the number of conflict constraints an have more than doubled the size of the maximum clique. The improved mixed integer model comprises fewer constraints and is therefore more memory-efficient than the model presented after the competition. We propose valid inequalities based on cliques and a Data-dependent Dual-Feasible Function (DDFF) to enhance our model. We run the tests on the twelve instances presented in the competition and the Yeditepe instances. The problem contains several criteria, whichwere also tested individually to help end users decide their respective importance. When our model and the original model are compared on the different instances,results show that the improved model yields better results for the majority of thecases and uses less memory