Parallel Design of a GPU-Resident Semi-Lagrangian Drift-Kinetic Solver on Unstructured Extruded Tokamak Meshes

Abstract

Semi-Lagrangian (SL) schemes advect a distribution function along characteristics and remap it to a fixed grid. They are unconditionally stable without a global solve, and with discontinuous Galerkin (DG) integration the transfer along a magnetic field line conserves mass exactly. This paper presents the parallel and GPU design of a 3X+2V SLDG drift-kinetic tokamak solver on unstructured, flux-surface-aligned poloidal planes of shaped cross section, extruded toroidally. Transport follows magnetic field lines across the planes, and each velocity channel advances a fixed distance per step, proportional to its parallel speed, so the halo depth a channel needs grows with its speed. Velocity-dependent ragged halos exploit this, sending each channel only its own upwind depth. The 4D decomposition includes the toroidal angle, the 2D poloidal plane and the magnetic moment, and leaves the parallel velocity whole: no stage transports across the magnetic moment, while a parallel-velocity partition would put a halo inside the acceleration stage. On NVIDIA A100s the design strong-scales over the magnetic-moment axis from one to 12 four-GPU nodes, and a weak series of three points refining all five phase-space dimensions together, 16x in total per series point, holds a weak-scaling efficiency of 75% on 16 GPUs and 57% on 256, from a one-GPU base case. The pointwise interpolations within the poloidal plane do not conserve mass, and the full step's mass drift stays below 2.1x10^-5 at every series point. The design was implemented with an AI code assistant under a machine-checked regression discipline, in which every change is held to one of four exactness classes, from bit-identical to a physics rate within a stated tolerance.