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Section: New Software and Platforms
FreeFem++ Toolboxes
Shape optimization toolbox in FreeFem++
Participants : Grégoire Allaire, Olivier Pantz.
We propose several FreeFem++ routines which allow the users to optimize the thickness, the geometry or the topology of elastic structures. All examples are programmed in two space dimensions. These routines have been written by G. Allaire, B. Boutin, C. Dousset, O. Pantz. A web page of this toolbox is available at http://www.cmap.polytechnique.fr/~allaire/freefem_en.html .
We also have written a C++ code to solve the Hamilton Jacoby equation used in the Level-set shape optimization method. This code has been linked with FreeFem++ routines.
Eddy current problems
Participants : Zixian Jiang, Mohamed Kamel Riahi.
We developed a FreeFem++ toolbox that solves direct and inverse problems for an axisymmetric and 3D eddy current problems related to non destructive testing of deposits on the shell side of PWR fuel tubes. For the 3-D version, one can refer to http://www.cmap.polytechnique.fr/~riahi and also to [15] .
Contact managements
Participant : Olivier Pantz.
We have developed a toolbox running under Freefem++ in order to take into account the non-intersection constraints between several deformable bodies. This code has been used to treat contacts between red blood cells in our simulations, but also between genuine non linear elastic structure. It can handle both contacts and self-contacts.
Moreover, a toolbox based on the Penalization method has also been developed.
De-Homogenization
Participant : Olivier Pantz.
We have developed a code under Freefem++ that implements our De-Homogenization method. It has been used to solve the compliance minimization problem of the compliance of an elastic shape. In particular, it enables us to recover well known optimal Michell's trusses for shapes of low density.