Abstract

Many systems in plasma physics are most accurately described by the Boltzmann equation, which determines the time evolution of the phase space distribution function of the system. Since this distribution function is a function of six variables, numerical schemes relying entirely on the discretization of the distribution function on a grid are often prohibitively expensive in terms of memory and run-time complexity. Monte-Carlo methods have a computational cost that scales better with the number of dimensions of the system, and are therefore favored. In particular, one of the most popular methods in plasma physics is the Particle-In-Cell method (PIC), which is a hybrid scheme combining a Monte-Carlo approach for velocity space with a grid discretization for configuration space. A weakness of all PIC schemes is that they require a very large number of simulation particles in order to limit the error due to statistical noise inherently associated with any Monte-Carlo approach. Computer simulations of kinetic plasmas thus remain very expensive regardless of the chosen numerical scheme, often of the order of days and sometimes weeks on the largest supercomputers in the world. In this talk, I will discuss a rigorous method based on the sparse grids combination technique [1,2] to reduce the numerical noise in PIC simulations of plasmas, and thus significantly reduce the number of simulation particles without sacrificing the accuracy of the solution.