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Title: Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport

Abstract

The NEWTRNX transport module solves the multigroup, discrete-ordinates source-driven or k-eigenvalue transport equation in parallel on a 3-D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slice-balance approach (SBA), spatial discretization. The spatial domains are decomposed using METIS. NEWTRNX is under development for nuclear reactor analysis on computer hardware ranging from clusters to massively parallel machines, like the Cray XT4. Transport methods that rely on full sweeps across the spatial domain have been shown to display poor scaling for thousands of processors. The Parallel Block-Jacobi (PBJ) algorithm allows each spatial partition to sweep over all discrete-ordinate directions and energies independently of all other domains, potentially allowing for much better scaling than possible with full sweeps. The PBJ algorithm has been implemented in NEWTRNX using a Gauss-Seidel iteration in energy and an asynchronous communication by an energy group, such that each partition utilizes the latest boundary solution available for each group before solving the withingroup scattering in a given group. For each energy group, the within-group scattering converges with a generalized minimum residual (GMRES) solver, preconditioned with beta transport synthetic acceleration ({beta}-TSA).

Authors:
 [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
958802
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: ANS2007 Winter Meeting, Washington, DC, USA, 20071111, 20071115
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCELERATION; ALGORITHMS; COMMUNICATIONS; COMPUTERS; DISCRETE ORDINATE METHOD; IMPLEMENTATION; REACTORS; SCATTERING; TRANSPORT

Citation Formats

Clarno, Kevin T. Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport. United States: N. p., 2007. Web.
Clarno, Kevin T. Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport. United States.
Clarno, Kevin T. Mon . "Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport". United States. doi:.
@article{osti_958802,
title = {Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport},
author = {Clarno, Kevin T},
abstractNote = {The NEWTRNX transport module solves the multigroup, discrete-ordinates source-driven or k-eigenvalue transport equation in parallel on a 3-D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slice-balance approach (SBA), spatial discretization. The spatial domains are decomposed using METIS. NEWTRNX is under development for nuclear reactor analysis on computer hardware ranging from clusters to massively parallel machines, like the Cray XT4. Transport methods that rely on full sweeps across the spatial domain have been shown to display poor scaling for thousands of processors. The Parallel Block-Jacobi (PBJ) algorithm allows each spatial partition to sweep over all discrete-ordinate directions and energies independently of all other domains, potentially allowing for much better scaling than possible with full sweeps. The PBJ algorithm has been implemented in NEWTRNX using a Gauss-Seidel iteration in energy and an asynchronous communication by an energy group, such that each partition utilizes the latest boundary solution available for each group before solving the withingroup scattering in a given group. For each energy group, the within-group scattering converges with a generalized minimum residual (GMRES) solver, preconditioned with beta transport synthetic acceleration ({beta}-TSA).},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

Conference:
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  • This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of themore » GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations will be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D{sup FD}) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method.« less
  • A Fourier analysis is conducted for the discrete-ordinates (SN) approximation of the neutron transport problem solved with Richardson iteration (Source Iteration) and Richardson iteration preconditioned with Transport Synthetic Acceleration (TSA), using the Parallel Block-Jacobi (PBJ) algorithm. Both 'traditional' TSA (TTSA) and a 'modified' TSA (MTSA), in which only the scattering in the low order equations is reduced by some non-negative factor {beta} and < 1, are considered. The results for the un-accelerated algorithm show that convergence of the PBJ algorithm can degrade. The PBJ algorithm with TTSA can be effective provided the {beta} parameter is properly tuned for a givenmore » scattering ratio c, but is potentially unstable. Compared to TTSA, MTSA is less sensitive to the choice of {beta}, more effective for the same computational effort (c'), and it is unconditionally stable. (authors)« less
  • A new nonlinear coarse-mesh rebalance (CMR) method is developed and tested to accelerate the one- and two-dimensional discrete ordinates neutron transport calculations. The method is based on rebalance factors that are angular dependent and defined on the coarse-mesh boundaries only. Unlike the conventional CMR method that is only conditionally stable, Fourier analysis and numerical tests show that this coarse-mesh angular dependent rebalance (CMADR) method is unconditionally stable for any optical thickness, scattering ratio, and coarseness and that the acceleration is very effective in most cases.
  • The coarse-mesh rebalance method is adopted in Monte Carlo schemes for aiming at accelerating the convergence of a source iteration process to obtain the eigenvalue of a nuclear reactor system. At every completion of the Monte Carlo game for one batch of neutron histories, the scaling factor for the neutron flux is calculated to achieve the neutron balance in each coarse-mesh zone. This rebalance factor is multiplied to the weight of each fission neutron in the coarse-mesh zone for playing the next Monte Carlo game. The numerical examples show that the present rebalance method gives a new usable sampling techniquemore » to get a better estimate of the number of neutrons lost or produced in each coarse- mesh zone by modifying the value obtained directly from the normal Monte Carlo calculation.« less