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Section: Application Domains

Numerical simulation

flow simulation for oil exploration: we co-advised three Ph.D. theses with the Gocad Consortium, that develops modeling algorithms for oil and gas exploration. We developed specialized meshing algorithms, well suited to represent geological layers at various resolutions [27] , [19] .

optimal transport: this is an active research topics in the mathematics community. Given two measures $\mu$ and $\nu$, optimal transport defines a distance between $\mu$ and $\nu$, as the minimum cost of “morphing” $\mu$ into $\nu$. This distance (called the Wasserstein distance) structures the space of measures and offers new ways of solving some highly non-linear PDEs (Monge-Ampere, Fokker-Plank ...). This requires a numerical way of computing the Wasserstein distance and its gradients. We studied a semi-discrete technique [21] (conditionally accepted to ESAIM J. M2AN) that optimizes power diagrams. This is to our knowledge the first numerical implementation of optimal transport for volumetric densities (computes the Wasserstein distance between a sum of Dirac masses and a piece-wise linear density supported on a tetrahedral mesh).

Bose-Einstein condensates: Xavier Antoine (prof. in mathematics at the Université de Lorraine) joined the team on a “delegation” position (Sept. 2013 - Sept. 2014) to explore some common research topics. We are members of the BECASIM project, funded by the ANR (“French NSF”). In a certain sense, a Bose-Einstein condensate is a “Schroedinger cat” made of a few hundred atoms. By special physical means (low temperature and lasers), the probability waves of these atoms are intermixed, thus forming an alternative state of matter. The BECASIM project aims at developing numerical simulation methods for these complicated phenomena (that intermix fluid dynamics, electromagnetics and quantum physics).