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

Abstract

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 themore » 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.« less

Authors:
ORCiD logo [1];  [2];  [2]
  1. Univ. of Michigan, Ann Arbor, MI (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Michigan, Ann Arbor, MI (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1527282
Report Number(s):
LLNL-JRNL-759325
Journal ID: ISSN 0029-5639; 947672
Grant/Contract Number:  
AC52-07NA27344; AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 193; Journal Issue: 7; Journal ID: ISSN 0029-5639
Publisher:
American Nuclear Society - Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
CMFD; Multilevel; Eigenvalue; 3-D; Multigroup

Citation Formats

Yee, Ben C., Kochunas, Brendan, and Larsen, Edward W. A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems. United States: N. p., 2019. Web. doi:10.1080/00295639.2018.1562777.
Yee, Ben C., Kochunas, Brendan, & Larsen, Edward W. A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems. United States. doi:10.1080/00295639.2018.1562777.
Yee, Ben C., Kochunas, Brendan, and Larsen, Edward W. Wed . "A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems". United States. doi:10.1080/00295639.2018.1562777.
@article{osti_1527282,
title = {A Multilevel in Space and Energy Solver for 3-D Multigroup Diffusion and Coarse-Mesh Finite Difference Eigenvalue Problems},
author = {Yee, Ben C. and Kochunas, Brendan and Larsen, Edward W.},
abstractNote = {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.},
doi = {10.1080/00295639.2018.1562777},
journal = {Nuclear Science and Engineering},
issn = {0029-5639},
number = 7,
volume = 193,
place = {United States},
year = {2019},
month = {2}
}

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