Mathematics

Optimal urban mobility network design for sustainable space sharing between vehicles and soft transport modes

Nowadays, we are witnessing a rapid spread of multimodal mobility in our cities and a willingness on the part of communities to promote new mobility behaviors. These changes are causing road networks to evolve and grow with modifications that are often far from being optimally designed, and public authorities are beginning to investigate how to integrate new paths and roads for the new soft transportation modes (bicycles, e-scooters, etc.).

Hybrid High-Order methods for Phase-field modeling of fracture propagation

In this thesis, we are interested in the modeling of fracture propagation. Historical formulations have two types of drawbacks. In the case of local damage models, the limitations come from the fact that the results depend on the computational mesh. On the other hand, when each fracture is modeled independently, the limiting factor is the computational cost. The phase-field fracture modeling method has the advantage of being a continuous method that integrates naturally with Continuous Media Mechanics and the associated numerical tools.

Scenario tree reduction and operator decomposition method for stochastic optimization of energy systems

The drop in production costs of distributed energy production systems and electrochemical storage systems coupled with the evolution of regulations make it possible to build local energy management operations. Development of such operations will be all the easier if the management systems allow the various involved players to reduce their electricity bills and/or their greenhouse gas emissions To this end, the various energy systems need to be optimized, a challenging task for mainly two reasons: First, the random nature of consumption/production.