香蕉视频

Alexei Lozinski
University Paul Sabatier (Toulouse 3)

We present an adaptation of a multiscale finite element method (MsFEM) to the solution of a diffusion equations in domains with multiple holes or cracks. To avoid the use of a complex unstructured mesh that perfectly fits the geometry of the boundary a penalization technique can be used. We shall compare a direct application of the MsFEM on the perforated domain and its combination with the penalization approach. The disadvantage of the direct method (apart from the use of complex meshes) consists in the necessity to develop new oversampling methods which turn out to be less efficient than the classical oversempling technique applied to the penalized problem. We shall also present new variants of MsFEM inspired by the non conforming finite elements 脿 la Crouzeix-Raviart. We present numerical results for academic test cases inspired by homogeneization theory and for the problem of pollution spreading in urban areas. In the last case, the goal of the MsFEM is to be able to perform a fast real time computation on a genuine urban area. Other possible applications include analysis of perforated or cracked materials, air flow inside a cockpit, and so on.