A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

Journal Article · 09 November 2023 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2022.111747 · OSTI ID:2278785

Olivier, Samuel  ^[1]; Pazner, Will  ^[2]; Haut, Terry S. ^[3]; Yee, Ben C. ^[3]

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1. University of California, Berkeley, CA (United States)
2. Portland State University, OR (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
3. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S_N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC52-07NA27344; SC0019323; 20-ERD-002
• OSTI ID: 2278785
• Report Number(s): LLNL-JRNL-829396; 1042548; TRN: US2408660
• Journal Information: Journal of Computational Physics, Vol. 473; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English