Modeling and scientific computing

The research carried out in Modeling and Scientific Computing is related to applied mathematics and their interactions, with the objective of understanding phenomena through modeling, mathematical and numerical analysis, and the definition of efficient algorithms for computer simulation.

The models studied involve partial differential equations, probabilities, variational inequations, dynamical systems, multi-scale approaches, calculus of variations, etc.

The IMT brings together professors and researchers interested in Modeling & Scientific Computing in the PDE, Probability, Statistics/Optimization teams. There are mainly three thematic axes:

1) Engineering & Industry: this axis deals with problems in structural mechanics, fluid mechanics, imaging, data science and statistics. The contributions can be divided schematically into the following application areas

  • fluid/structure interactions: finite element method, variational inequations ;

  • wave propagation: Maxwell's and Helmholtz's equations;

  • imaging/machine learning: gradient methods, optimization, statistics;

  • relations with industry: ITM's valorization unit provides support to researchers and companies.

2) Applications to Physics: this axis covers a very broad spectrum mixing plasma physics, quantum physics, fluid mechanics, gas dynamics, and many interaction phenomena involving several states of matter.

  • plasma physics: kinetic equations (Vlasov-Poisson, Vlasov-Maxwell), MHD systems, magnetized plasmas, electric propulsion, atmospheric plasmas;

  • fluid mechanics: compressible fluids, shock waves, flow stability, gas dynamics (Boltzmann equation);

  • numerical methods for dispersive equations (Schrödinger equation, KdV, applications to quantum physics, mathematical physics).

3) Biology & Health: this axis is concerned with questions arising from ecology, biology and medicine. Three themes are privileged:

  • stochastic and deterministic modeling ;

  • mathematical methods for imaging ;

  • statistics for medicine and data science.

These activities are structured around the Math-Bio-Health Group.