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Title: A Monte Carlo synthetic-acceleration method for solving the thermal radiation diffusion equation

We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
Authors:
 [1] ;  [1] ;  [2] ;  [1]
  1. Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States)
  2. University of Wisconsin–Madison, 1500 Engineering Dr., Madison, WI 53716 (United States)
Publication Date:
OSTI Identifier:
22230858
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 258; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; ALGORITHMS; BENCHMARKS; DIFFUSION EQUATIONS; MATHEMATICAL SOLUTIONS; MATRICES; MONTE CARLO METHOD; THERMAL RADIATION