Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 344, Issue -, Pages 782-793Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2017.09.028
Keywords
Large-scale parallel iterative solvers; Fully-coupled algebraic multigrid preconditioners; Implicit finite element; Resistive MHD
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Funding
- DOE NNSA ASC Algorithms effort
- DOE Office of Science Applied Mathematics Program at Sandia National Labs
- U.S. Department of Energy's National Nuclear Security Administration [DE-NA-0003525]
- DOE Office of Science Applied Mathematics Program at Sandia National Laboratories [DE-AC04-94AL85000]
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This work explores the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid pre-conditioner. This study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of the original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Qplatform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system. (C) 2017 Elsevier B.V. All rights reserved.
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