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

Thomas M. Evans; Scott W. Mosher; Stuart R. Slattery; Steven P. Hamilton

doi:10.1016/j.jcp.2013.10.043

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

Thomas M. Evans, Scott W. Mosher, Stuart R. Slattery, Steven P. Hamilton

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	338-358
Number of pages	21
Journal	Journal of Computational Physics
Volume	258
DOIs	https://doi.org/10.1016/j.jcp.2013.10.043
State	Published - Feb 1 2014

Funding

Work for this paper was supported by Oak Ridge National Laboratory , which is managed and operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract No. DEAC05-00OR22725 . The early part of this work was performed at Los Alamos National Laboratory under U.S. Government contract W-7405-ENG-36 .

Keywords

Monte Carlo
Radiation diffusion
Sparse matrix systems
Synthetic acceleration

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10.1016/j.jcp.2013.10.043

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abstract = "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.",

keywords = "Monte Carlo, Radiation diffusion, Sparse matrix systems, Synthetic acceleration",

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AU - Evans, Thomas M.

AU - Mosher, Scott W.

AU - Slattery, Stuart R.

AU - Hamilton, Steven P.

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Y1 - 2014/2/1

N2 - 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.

AB - 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.

KW - Monte Carlo

KW - Radiation diffusion

KW - Sparse matrix systems

KW - Synthetic acceleration

UR - https://www.scopus.com/pages/publications/84887575865

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SP - 338

EP - 358

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

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

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