Numerical Simulation, Optimisation and Control
Mathematical modeling is at the core of all engineering fields. The development of extremely powerful computing systems has allowed the simulation of models that were out of reach a few decades ago. Once a mathematical model is available, it is also possible to optimize the system, evaluate its properties or design controlers.
ptimization models therefore arise in a variety of fields of engineering : machine learning, energy management, data analysis, biomedical engineering among others. Because not all optimization models can be solved efficiently, it is important to formulate the problems in a way that leads to tractable models, sometimes accepting to solve an approximation of the initial problem at hand. The models that we are interested in are tractable from the practical point of view and are either linear, convex or mixed-integer. The research carried out in the department is about the optimization algorithms themselves as well as finding the right formulations for a series of problems arising in all other domains of applications of the department.
We are also active in developing numerical methods for evaluating the electrical, magnetic, electromagnetic, and thermal behavior of systems, with an approach that combines applied mathematical techniques with models of the physical or biophysical properties of the systems. We have also developed and implemented numerical methods for efficient dynamic simulation of large electric power systems modeled by differential-algebraic equations. They combine domain decomposition, localization, and parallel processing techniques. They have been applied to real-life distribution and transmission power systems.
We are also active in developing numerical methods for evaluating the electrical, magnetic, electromagnetic, acoustic and thermal behavior of systems