Numerical models and mathematical methods
Together with the increase in computing power (Moore's Law), the mathematical and numerical techniques used to resolve the equations from physical models have progressed greatly, despite the many difficulties related to the complexity and non-linearity of these models.
Examples include the methods for hyperbolic systems and gas dynamics, for transport and diffusion equations and for coupled systems. New techniques have been able to improve precision whilst preserving robustness. Dynamic adaptation of meshes, by refining or unrefining, is a good example. Front-capture techniques are another example, without forgetting the various finite element methods. For transport equations, improvements relate to both the statistical (Monte Carlo) and deterministic approaches. We could also consider the algorithms for efficient resolution of large linear systems, or the techniques for evaluating the uncertainties and sensitivity of the simulation parameters.
This progress in numerical models and mathematical methods comes from a continuous research effort aimed at applied mathematics, numerical analysis and computer science. This research is performed in cooperation with the various research communities concerned: university laboratories, other higher education institutes and research organisations. This can lead to more formal collaborations. The research is illustrated by internationally reviewed publications and conference presentations. It is also manifest in the supervision of trainees (Masters and third year engineering students), graduate students and postdoctoral researchers.