A Multilevel in Space and Energy Solver for 3D Multigroup Diffusion and CoarseMesh 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 lowerorder equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (onegroup) diffusion eigenvalue problem that is solved via Wielandtshifted power iteration (PI) and (2) a multigridinspace linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a onedimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarsemesh finite difference (CMFD) system in the threedimensional 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 »
 Authors:

 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)
 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):
 LLNLJRNL759325
Journal ID: ISSN 00295639; 947672
 Grant/Contract Number:
 AC5207NA27344; AC0500OR22725
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 193; Journal Issue: 7; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 CMFD; Multilevel; Eigenvalue; 3D; Multigroup
Citation Formats
Yee, Ben C., Kochunas, Brendan, and Larsen, Edward W. A Multilevel in Space and Energy Solver for 3D Multigroup Diffusion and CoarseMesh 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 3D Multigroup Diffusion and CoarseMesh 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 3D Multigroup Diffusion and CoarseMesh Finite Difference Eigenvalue Problems". United States. doi:10.1080/00295639.2018.1562777.
@article{osti_1527282,
title = {A Multilevel in Space and Energy Solver for 3D Multigroup Diffusion and CoarseMesh 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 lowerorder equations with only one group and/or coarser spatial grids. It consists of two primary components: (1) a grey (onegroup) diffusion eigenvalue problem that is solved via Wielandtshifted power iteration (PI) and (2) a multigridinspace linear solver. In previous work, the efficiency of MSED was verified using Fourier analysis and numerical results from a onedimensional multigroup diffusion code. Since that work, MSED has been implemented as a solver for the coarsemesh finite difference (CMFD) system in the threedimensional 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 wellconverged 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 MSEDL) to circumvent the issue until the multiphysics iteration in MPACT is improved. Results show that MSEDL 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 = {00295639},
number = 7,
volume = 193,
place = {United States},
year = {2019},
month = {2}
}