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Thursday, February 21

Asymptotic Preserving Implicit-Explicit Runge-Kutta
Methods For Nonlinear Kinetic Equations

Giacomo Dimarco, University Paul Sabatier, Toulouse III, France
Computer Science and Mathematics Division Seminar
10:00 AM — 11:00 AM, Joint Institute for Computational Sciences (Building 5100), Auditorium (Room 128)
Contact: Cory Hauck (, 865.574.0730


In this talk, we will discuss Implicit-Explicit (IMEX) Runge Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We will consider both the case of easy invertible collision operators and the challenging case of Boltzmann collision operators. We give sufficient conditions in order that such methods are asymptotic preserving and asymptotically accurate. Their monotonicity properties are also studied. In the case of the Boltzmann operator the methods are based on the introduction of a penalization technique for the collision integral. This reformulation of the collision operator permits to construct penalized IMEX schemes which work uniformly for a wide range of relaxation times, avoiding the expensive implicit resolution of the collision operator. Finally we show some numerical results which confirm the theoretical analysis.