A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation
Abstract
We present a novel synthetic-acceleration based Monte Carlo method for solving the equilibrium thermal radiation diusion equation in three 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 not only can our Monte Carlo method be an eective solver for sparse matrix systems, but also that it performs competitively with deterministic methods including preconditioned Conjugate Gradient while producing numerically identical results. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
- Authors:
-
- ORNL
- University of Wisconsin, Madison
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- Work for Others (WFO)
- OSTI Identifier:
- 1105918
- DOE Contract Number:
- DE-AC05-00OR22725
- Resource Type:
- Journal Article
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 258; Journal ID: ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
- Subject:
- radiation diffusion; synthetic acceleration; Monte Carlo; sparse matrix systems
Citation Formats
Evans, Thomas M, Mosher, Scott W, and Slattery, Stuart. A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation. United States: N. p., 2014.
Web. doi:10.1016/j.jcp.2013.10.043.
Evans, Thomas M, Mosher, Scott W, & Slattery, Stuart. A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation. United States. https://doi.org/10.1016/j.jcp.2013.10.043
Evans, Thomas M, Mosher, Scott W, and Slattery, Stuart. 2014.
"A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation". United States. https://doi.org/10.1016/j.jcp.2013.10.043.
@article{osti_1105918,
title = {A Monte Carlo Synthetic-Acceleration Method for Solving the Thermal Radiation Diffusion Equation},
author = {Evans, Thomas M and Mosher, Scott W and Slattery, Stuart},
abstractNote = {We present a novel synthetic-acceleration based Monte Carlo method for solving the equilibrium thermal radiation diusion equation in three 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 not only can our Monte Carlo method be an eective solver for sparse matrix systems, but also that it performs competitively with deterministic methods including preconditioned Conjugate Gradient while producing numerically identical results. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.},
doi = {10.1016/j.jcp.2013.10.043},
url = {https://www.osti.gov/biblio/1105918},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 258,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 2014},
month = {Wed Jan 01 00:00:00 EST 2014}
}
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