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Collisional processes are critical in the understanding of non-Maxwellian plasmas. The Landau form of the Fokker-Planck equation is the gold standard for modeling collisions in most plasmas, however <tex>$\mathcal{O}(N^{2})$</tex> work complexity inhibits its widespread use. We show that with advanced numerical methods and GPU hardware this cost can be effectively mitigated. This paper extends previous work on a conservative, high order accurate, finite element discretization with adaptive mesh refinement of the Landau operator, with extensions to GPU hardware and implementations in both the CUDA and Kokkos programming languages. This work focuses on the Landau kernels and on NVIDIA hardware, however preliminary results on AMD and Fujitsu/ARM hardware, as well as end-to-end performance of a velocity space model of a plasma thermal quench, are also presented. Both the fully implicit Landau time integrator and the plasma thermal quench model are publicly available in PETSc (Portable, Extensible, Toolkit for Scientific computing).

Landau collision operator in the CUDA programming model applied to thermal quench plasmas