A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

Yee, Ben C.; Kochunas, Brendan; Larsen, Edward W.

doi:10.1080/00295639.2018.1562777

Title: A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems

Journal Article · Wed Feb 13 00:00:00 EST 2019 · Nuclear Science and Engineering

DOI:https://doi.org/10.1080/00295639.2018.1562777· OSTI ID:1527282

^[1]; Kochunas, Brendan ^[2]; Larsen, Edward W. ^[2]

Univ. of Michigan, Ann Arbor, MI (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)

The Multilevel in Space and Energy Diffusion (MSED) method accelerates the iterative convergence of multigroup diffusion eigenvalue problems by performing work on lower-order equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (one-group) diffusion eigenvalue problem that is solved via Wielandt-shifted power iteration (PI) and (2) a multigrid-in-space linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a one-dimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarse-mesh finite difference (CMFD) system in the three-dimensional Michigan Parallel Characteristics Transport (MPACT) code. In this paper, the results from the implementation of MSED in MPACT are introduced, and the changes needed to make MSED more suitable for MPACT are described. For problems without feedback, the conclusions in this paper show that MSED can reduce the CMFD run time by an order of magnitude and the overall run time by a factor of 2 to 3 compared to the default CMFD solver in MPACT [PI with the generalized minimal residual (GMRES) method]. For problems with feedback, the convergence of the outer Picard iteration scheme is worsened by the well-converged CMFD solutions produced by the standard MSED method. To overcome this unintuitive deficiency, MSED may be run with looser convergence criteria (a modified version of the MSED method called MSED-L) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSED-L can reduce the CMFD run time in MPACT by an order of magnitude, without negatively impacting the outer Picard iteration scheme.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344; AC05-00OR22725

OSTI ID:: 1527282

Report Number(s):: LLNL-JRNL-759325; 947672

Journal Information:: Nuclear Science and Engineering, Vol. 193, Issue 7; ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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