**Abstract**: Projective integration has recently been proposed as a viable alternative to fully implicit and micro-macro methods for providing light, nonintrusive and almost asymptotic preserving integrators for collisional kinetic equations. In this talk, we shall present fully explicit projective integration and telescopic projective integration schemes for the multispecies Boltzmann and the Bhatnagar, Gross, and Krook equations. The methods employ a sequence of small forward-Euler steps, intercalated with large extrapolation steps. The telescopic approach repeats said extrapolations as the basis for an even larger step. This hierarchy renders the computational complexity of the method essentially independent of the stiffness of the problem, which permits the efficient solution of equations in the hyperbolic scaling with very small Knudsen numbers. We validate the schemes on a range of scenarios, demonstrating its prowess in dealing with extreme mass ratios, fluid instabilities, and other complex phenomena. This is a joint work with R. Bailo from the University of Oxford, as well as W. Melis and G. Samaey from Katholieke Universiteit Leuven.

**Speaker’s Bio**: Since September 2014, Thomas Rey has been a tenured Assistant Professor (Maitre de conférence) in applied mathematics and high performance computing in the mathematics Department at Université de Lille, the largest French university. Before that, from September 2012 to September 2014, he was a Research Associate at the Center for Scientific Computation and Mathematical Modeling of the University of Maryland, College Park. He did his Ph.D. program from 2009 to 2012 at Université Claude Bernard Lyon, under the supervision of Francis Filbet (now in Université Toulouse 2) and Clément Mouhot (now at the University of Cambridge).

Last Updated: April 8, 2022 - 10:35 am