A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems
Abstract
We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.
- Authors:
- Publication Date:
- Research Org.:
- UT-Battelle LLC/ORNL, Oak Ridge, TN (Unted States), Oak Ridge National Laboratory, Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1567361
- DOE Contract Number:
- AC05-00OR22725
- Resource Type:
- Conference
- Journal Name:
- SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO
- Additional Journal Information:
- Conference: Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2013, Paris, France, October 27-31, 2013
- Country of Publication:
- United States
- Language:
- English
- Subject:
- Computer Science; Nuclear Science & Technology
Citation Formats
Slattery, Stuart R., Evans, Thomas M., Wilson, Paul P.H., Caruge, D., Calvin, C., Diop, C.M., Malvagi, F., and Trama, J.-C. A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems. United States: N. p., 2014.
Web. doi:10.1051/snamc/201404211.
Slattery, Stuart R., Evans, Thomas M., Wilson, Paul P.H., Caruge, D., Calvin, C., Diop, C.M., Malvagi, F., & Trama, J.-C. A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems. United States. doi:10.1051/snamc/201404211.
Slattery, Stuart R., Evans, Thomas M., Wilson, Paul P.H., Caruge, D., Calvin, C., Diop, C.M., Malvagi, F., and Trama, J.-C. Wed .
"A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems". United States. doi:10.1051/snamc/201404211.
@article{osti_1567361,
title = {A Multiple-Set Overlapping-Domain Decomposed Monte Carlo Synthetic Acceleration Method for Linear Systems},
author = {Slattery, Stuart R. and Evans, Thomas M. and Wilson, Paul P.H. and Caruge, D. and Calvin, C. and Diop, C.M. and Malvagi, F. and Trama, J.-C.},
abstractNote = {We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.},
doi = {10.1051/snamc/201404211},
journal = {SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO},
number = ,
volume = ,
place = {United States},
year = {2014},
month = {1}
}
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Works referenced in this record:
Matrix Inversion by a Monte Carlo Method
journal, July 1950
- Forsythe, George E.; Leibler, Richard A.
- Mathematical Tables and Other Aids to Computation, Vol. 4, Issue 31
Sequential Monte Carlo
journal, January 1962
- Halton, J. H.
- Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 58, Issue 1
Sequential monte carlo techniques for the solution of linear systems
journal, June 1994
- Halton, John H.
- Journal of Scientific Computing, Vol. 9, Issue 2
Hybrid and Parallel Domain-Decomposition Methods Development to Enable Monte Carlo for Reactor Analyses
journal, January 2011
- Wagner, John C.; Mosher, Scott W.; Evans, Thomas M.
- Progress in Nuclear Science and Technology, Vol. 2, Issue 0
An efficient, robust, domain-decomposition algorithm for particle Monte Carlo
journal, June 2009
- Brunner, Thomas A.; Brantley, Patrick S.
- Journal of Computational Physics, Vol. 228, Issue 10
Efficient parallel Monte Carlo methods for matrix computations
journal, August 1998
- Alexandrov, V. N.
- Mathematics and Computers in Simulation, Vol. 47, Issue 2-5
Comparison of four parallel algorithms for domain decomposed implicit Monte Carlo
journal, March 2006
- Brunner, Thomas A.; Urbatsch, Todd J.; Evans, Thomas M.
- Journal of Computational Physics, Vol. 212, Issue 2
Analysis of communication costs for domain decomposed Monte Carlo methods in nuclear reactor analysis
journal, April 2012
- Siegel, A.; Smith, K.; Fischer, P.
- Journal of Computational Physics, Vol. 231, Issue 8
An overview of the Trilinos project
journal, September 2005
- Heroux, Michael A.; Phipps, Eric T.; Salinger, Andrew G.
- ACM Transactions on Mathematical Software, Vol. 31, Issue 3