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Title: Implementation of Transport Synthetic Acceleration in NEWTRNX

Abstract

NEWTRNX is a 3-D deterministic transport solver under development to solve large problems using spatial partitioning with Parallel Block Jacobi iteration structure; it employs the Slice-Balance Approach to sweep across a tetrahedral mesh on each partition independently. The innermost iteration, operating on a single partition, solves a one-group transport equation that stores only the volumetric flux moments and the angular flux on boundary faces.

Authors:
 [1];  [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:
958797
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: American Nuclear Society 2007 Winter Meeting, Washington, DC, USA, 20071111, 20071115
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCELERATION; IMPLEMENTATION; TRANSPORT

Citation Formats

Clarno, Kevin T, and Johnson, Seth R. Implementation of Transport Synthetic Acceleration in NEWTRNX. United States: N. p., 2007. Web.
Clarno, Kevin T, & Johnson, Seth R. Implementation of Transport Synthetic Acceleration in NEWTRNX. United States.
Clarno, Kevin T, and Johnson, Seth R. Mon . "Implementation of Transport Synthetic Acceleration in NEWTRNX". United States. doi:.
@article{osti_958797,
title = {Implementation of Transport Synthetic Acceleration in NEWTRNX},
author = {Clarno, Kevin T and Johnson, Seth R},
abstractNote = {NEWTRNX is a 3-D deterministic transport solver under development to solve large problems using spatial partitioning with Parallel Block Jacobi iteration structure; it employs the Slice-Balance Approach to sweep across a tetrahedral mesh on each partition independently. The innermost iteration, operating on a single partition, solves a one-group transport equation that stores only the volumetric flux moments and the angular flux on boundary faces.},
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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  • We present a new class of synthetic acceleration methods which can be applied to transport calculations regardless of geometry, discretization scheme, or mesh shape. Unlike other synthetic acceleration methods which base their acceleration on P1 equations, these methods use acceleration equations obtained by projecting the transport solution onto a coarse angular mesh only on cell boundaries. We demonstrate, via Fourier analysis of a simple model problem as well as numerical calculations of various problems, that the simplest of these methods are unconditionally stable with spectral radius less than or equal toc/3 (c being the scattering ratio), for several different discretizationmore » schemes in slab geometry. 28 refs., 4 figs., 3 tabs.« less
  • In the past several years, diffusion-synthetic acceleration (DSA) methods have proved useful for accelerating practical transport calculations; however, problems still remain. The nonlinear methods have been applied only to a limited set of spatial discretizations and only on regular meshes. In addition they require positive fluxes, yet negative flux fixups can cause them to diverge. The linear methods are either limited to specific spatial discretizations, or yield acceleration equations that are so complicated in general that efficient solution methods have not yet been found. The authors present here a class of acceleration methods that can be applied to transport problems,more » regardless of geometry, mesh shape, or discretization scheme. It is shown that the simplest methods in this class are stable and effective and briefly discuss the question of efficiency.« less
  • The unconditionally stable diffusion-synthetic acceleration (DSA) methods of Alcouffe and Larsen utilize spatially discretized low-order (diffusion) equations that can be derived directly from the spatially discretized discrete ordinates equations. Extension of this procedure to higher order multidimensional differencing schemes (e.g., nodal discrete ordinates methods), however, yields low-order equations that appear to be much more difficult to solve efficiently, even when they are derived from the lowest order (constant-constant) two-dimensional nodal equations. The computationally efficient nodal DSA method developed by Khalil avoids this problem by relaxing the strict requirement that the discretized low-order equations be derived directly from the discrete ordinatesmore » equations. Here, the authors develop an interface-current synthetic acceleration (ICSA) method that differs from previous work in two respects: (a) the low-order equations (which can be derived directly from the discretized transport equation) are based on a double P/sub 0/ representation of the angular fluxes on the cell boundaries only, and (b) the final synthetic equations retain the relatively simple structure of traditional interface-current equations. Adams and Martin have independently developed and Fourier-analyzed a general approach to synthetic acceleration that also uses half-range approximations to the interface angular fluxes.« less
  • The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observedmore » to be less effective in higher dimensions. This is due in part to the expense of solving the related diffusion linear system. We investigate here the effectiveness of a parallel semicoarsening multigrid (SMG) solution approach to DSA preconditioning in several three dimensional problems. In particular, we consider the algorithmic and implementation scalability of a parallel SMG-DSA preconditioner on several types of test problems.« less
  • Some modifications of the Diffusion Synthetic Acceleration (DSA) technique are proposed to face its loss of effectiveness when dealing with highly anisotropic scattering. A model case convergence analysis of the proposed techniques is performed; an extensive set of comparisons with results obtained by means of already assessed DSA modification techniques is reported for various scattering cross-section configurations. The importance of non asymptotic convergence velocity as a theoretical means to characterize and optimize different acceleration methods is also discussed.