Codes

Boundary integral methods for elasticity around a crack network
Project financed by: LJLL-UPMC and IFPEN (Institut Français du Pétrole Énergies Nouvelles)
Supervisors: Xavier Claeys, Ibtihel Ben Gharbia, Pierre-Henri Tournier
In the framework of the summer school CEMRACS 2016 (Numerical challenges in parallel scientific computing), I worked on the project ElastoPhi, together with Pierre Marchand.

We studied an elastostatic problem arising from industrial applications of IFPEN, posed at the surface of highly irregular crack networks. The discretization of the boundary integral equations of the model leads to dense matrices, which would imply high computational costs. In order to reduce these costs, we implemented a complexity reduction technique based on the Adaptive Cross Approximation (ACA) combined with hierarchical matrices.

Our C++ library is available here. For more details see the corresponding proceedings.

Edge finite elements are well suited for the approximation of the electric field in Maxwell's equations. During my PhD, I introduced into FreeFem++ the edge finite elements of degree 2 and 3 in 3D. FreeFem++ is an open source software developed by Frédéric Hecht.

You can use them in your .edp script with the keywords Edge13d, Edge23d, after writing load "Element_Mixte3d". See more details in this paper.

(The code of the underlying C++ plugin Element_Mixte3d.cpp is visible if FreeFem++ sources are downloaded and is thus found in the folder examples++-load.)