Alias-Free, Matrix-Free and Quadrature-Free Discontinuous Galerkin Algorithms for (Plasma) Kinetic Equations

Authors: Ammar Hakim (Princeton Plasma Physics Laboratory) and James Juno (University of Maryland)

Abstract: Understanding fundamental kinetic processes is important for many problems, from plasma physics to gas dynamics. A first-principles approach to these problems requires a statistical description via the Boltzmann equation, coupled to appropriate field equations. In this paper we present a novel version of the discontinuous Galerkin (DG) algorithm to solve such kinetic equations. Unlike Monte-Carlo methods we use a continuum scheme in which we directly discretize the 6D phase-space using discontinuous basis functions. Our DG scheme eliminates counting noise and aliasing errors that would otherwise contaminate the delicate field-particle interactions. We use modal basis functions with reduced degrees of freedom to improve efficiency while retaining a high formal order of convergence. Our implementation incorporates a number of software innovations; use of JIT compiled top-level language, automatically generated computational kernels and a sophisticated shared-memory MPI implementation; to handle velocity space parallelization.




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