A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

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• 作者：L. Chacó ; n ; ^{chacon@lanl.gov" class="auth_mail" title="E-mail the corresponding author} ; A. Stanier
• 关键词：Implicit algorithms ; Extended MHD ; JFNK ; Physics-based preconditioning ; Parallel multigrid
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：326
• 期：Complete
• 页码：763-772
• 全文大小：2083 K

文摘

We demonstrate a scalable fully implicit algorithm for the two-field low-β   extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096×4096$4096\times 4096$ mesh, we demonstrate a wall-clock-time speedup of ∼6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.