Two Approaches to Accelerated Monte Carlo Simulation of Coulomb Collisions

In plasma physics, the direct simulation of inter-particle Coulomb collisions is often necessary to capture the relevant physics, but presents a computational bottleneck because of the complexity of the process. In this thesis, we derive, test and discuss two methods for accelerating the simulation of collisions in plasmas in certain scenarios. The first is a hybrid fluid-Monte Carlo scheme that reduces the number of collisions that must be simulated. Coupling between the fluid and particle components of the scheme is accomplished by assigning to each particle a passive scalar approximating the relative entropy between its distribution of velocities and the fluid distribution. When this quantity is sufficiently small, the particle is moved into the fluid so its associated collisions need not be simulated. The second method is an adaptation of the multilevel Monte Carlo method. Instead of a single time step, this method introduces a hierarchy of time steps - i.e. levels - and uses the interplay between adjacent levels for variance reduction. We present new applications to plasmas, a method for eliminating the cost of the coarsest level calculation, and an alternative method for achieving the optimal overall computational complexity.Throughout, we discuss applications beyond plasma physics, including rarefied gases and chemical reaction networks.