SIAM seminar talk at University of Delaware
The University of Delaware chapter of SIAM was kind enough to invite me to speak about my research on dynamical low-rank methods for kinetic equations. The title of the talk was "Dynamical low-rank approximation for plasma kinetic model reduction".
Slides for the talk may be found here.
The Vlasov-Maxwell-Landau system can provide a high fidelity reproduction of plasma physics, but only at great computational cost. Classically, moment methods are used to reduce the 6 dimensional phase space problem to a 3 dimensional problem. However, conditions particular to plasmas, such as multiple species and magnetic field driven anisotropy, destroy the convergence of moment methods in many scenarios. Recently, the dynamical low rank method has been applied to kinetic simulation of plasmas, with promising results. We briefly review traditional moment methods and their shortcomings, then discuss the dynamical low rank method with special attention to the projection splitting integrator. We discuss an asymptotic-preserving integrator for the high-field limit of the Vlasov-Ampere system, a simplification of the Vlasov-Maxwell system. Special attention is paid to the IMEX time discretization of the projection splitting integrator.