Exponentially-convergent Monte Carlo for the 1-D transport equation
Abstract
We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)
- Authors:
-
- Department of Nuclear Engineering, TAMU 3133, Texas A and M University, College Station, TX 77843-3133 (United States)
- Publication Date:
- Research Org.:
- American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)
- OSTI Identifier:
- 22212809
- Resource Type:
- Conference
- Resource Relation:
- Conference: M and C 2013: 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, ID (United States), 5-9 May 2013; Other Information: Country of input: France; 9 refs.; Related Information: In: Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013| 3016 p.
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; CONVERGENCE; FINITE ELEMENT METHOD; MONTE CARLO METHOD; RESOLUTION; TRANSPORT THEORY
Citation Formats
Peterson, J. R., Morel, J. E., and Ragusa, J. C. Exponentially-convergent Monte Carlo for the 1-D transport equation. United States: N. p., 2013.
Web.
Peterson, J. R., Morel, J. E., & Ragusa, J. C. Exponentially-convergent Monte Carlo for the 1-D transport equation. United States.
Peterson, J. R., Morel, J. E., and Ragusa, J. C. 2013.
"Exponentially-convergent Monte Carlo for the 1-D transport equation". United States.
@article{osti_22212809,
title = {Exponentially-convergent Monte Carlo for the 1-D transport equation},
author = {Peterson, J. R. and Morel, J. E. and Ragusa, J. C.},
abstractNote = {We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)},
doi = {},
url = {https://www.osti.gov/biblio/22212809},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 2013},
month = {Mon Jul 01 00:00:00 EDT 2013}
}
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