Enhancing Particle-Based Kinetic Methods Through Multifidelity Discretizations
Bryan Reuter
Sandia National Laboratories
Center for Computing Research
Particle-based kinetic methods (e.g., particle-in-cell techniques) are commonly used for the simulation of non-equilibrium plasmas due to their relatively straightforward implementation and their avoidance of direct discretization of 6-dimensional phase space. Instead they employ a statistical approach, drawing a set of representative marker particles from the particle density function then evolving them in phase space according to collisions and self-consistent electromagnetic fields. As a Monte-Carlo technique, a major drawback is sampling noise and its slow convergence rate. This means it is often unfeasible to reach needed particle counts for certain problems even on large supercomputers.
In this talk we will discuss various approaches that attempt to overcome the issue of statistical noise and computational cost in particle-based kinetic methods. Our aim is to develop multifidelity methods that can enhance existing particle codes and allow for the simulation of strongly non-equilibrium plasmas at reduced cost. Many multifidelity approaches for noise reduction either explicitly assume weakly non-equilibrium behavior or are unstable outside of that regime. To this end, we discuss progress towards developing low-noise/low-cost methods that are suitable for large deviations from equilibrium.