Team defi

Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Contracts and Grants with Industry
Other Grants and Activities
Dissemination
Bibliography

Section: Software

FreeFem++ Toolboxes

Shape optimization in 2D (geometry and topology)

Participants : Olivier Pantz, Grégoire Allaire [correspondant] .

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 .

Shape optimization in 3D (geometry and topology)

Participant : Grégoire Allaire [correspondant] .

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 three space dimensions. These routines have been written by G. Allaire, A. Kelly. A web page of this toolbox is available at http://www.cmap.polytechnique.fr/~allaire/freefem3d.html .

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.

De-Homogenization

Participant : Olivier Pantz.

We have developed a code under Freefem++ that implements the De-Homogeneization 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.

Inverse shape problems for axisymmetric eddy current problems

Participants : Armin Lechleiter, Zixian Jiang.

This FreeFem++ toolbox solves inverse problems for an axisymmetric eddy current model using shape optimization techniques. The underlying problem is to find inclusions in a tubular and unbounded domain. The direct scattering problems are solved using an adaptive finite element method, and Dirichlet-to-Neumann operators are used to implement the transparent boundary conditions. Based on the shape derivative of an inclusion with respect to the domain, the toolbox offers regularized iterative algorithms to solve the inverse problem.


previous
next

Logo Inria