A selective discontinuous Galerkin implicit particle-in-cell method for plasma simulation with improved interpolation

This article dynamically incorporates multiple ideas into the existing direct implicit particle-in-cell (DIPIC) method for plasma simulation, in order to dramatically improve the DIPIC method for its local mesh refinement needs based on Cartesian meshes as well as its interpolation needs based on the locally refined meshes. One key tool is to utilize the selective discontinuous Galerkin method, which is based on the interior penalty discontinuous Galerkin formulation and the regular local finite element basis functions, as the electric field solver in the DIPIC simulation. This hybrid type finite element method combines the advantages of both continuous and discontinuous finite element basis functions. The use of the discontinuous basis functions in the selected areas will allow flexible local mesh refinements in the original Cartesian mesh, in order to capture the nonuniform or multi-scale phenomena of plasma in these areas, while the use of the continuous basis functions in other areas will significantly reduce the degree of freedom. An improved interpolation method is also developed to handle the interaction of particles with the locally refined meshes. Numerical experiments are provided to demonstrate the effectiveness of the improved DIPIC method.