April 4-6

Abstract Details

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Author: Jacob R King
Requested Type: Consider for Invited
Submitted: 2022-03-04 21:25:49

Co-authors: Sina Taheri, Eric Howell, Brian Cornille

Contact Info:
Tech-X Corp
5621 Arapahoe Ave Ste A
Boulder, Colorado   80303
United States

Abstract Text:
Incorporation of atomic physics associated with multiple species is required to study next-generation fusion device topics such as integration of MHD modeling of resonant magnetic perturbations or edge-harmonic oscillations with advanced edge solutions. The semi-implicit leapfrog time-discretization is a workhorse for initial-value MHD codes such as NIMROD and M3D-C1. By exploiting the functional structure of the MHD equations, the advances each field can be staggered or solved sequentially resulting in a smaller algebraic system during each separated field advance relative to the full system size. The inclusion of nonlinear atomic interactions breaks the functional structure of the MHD equations that is exploited by the leapfrog. We present an operator-splitting formulation of the atomic interactions using a Strang-splitting technique to naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. By testing on a battery of cases, we show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicholson with Newton iteration of the nonlinear terms. Since all of the nonlinear atomic interaction is handled by a local ODE solver using an Adams-Bashforth method, no nonlinear iteration is required and each spatial point can be treated independently and in parallel. This parallelism is advantageous for exploiting GPUs. We use OpenACC with a modern Fortran implementation using a continuous-integration development cycle to port NIMROD algorithms to the GPU architecture. The performance of the ported finite-element and matrix preconditioning kernels is reported. Finally, we show that for systems with multiple charged species the momentum equations can be transformed into a form with the charge-density-weighted terms from the center of mass equation and ODE coupling terms.