# 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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