# Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport

## Abstract

The NEWTRNX transport module solves the multigroup, discrete-ordinates source-driven or k-eigenvalue transport equation in parallel on a 3-D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slice-balance approach (SBA), spatial discretization. The spatial domains are decomposed using METIS. NEWTRNX is under development for nuclear reactor analysis on computer hardware ranging from clusters to massively parallel machines, like the Cray XT4. Transport methods that rely on full sweeps across the spatial domain have been shown to display poor scaling for thousands of processors. The Parallel Block-Jacobi (PBJ) algorithm allows each spatial partition to sweep over all discrete-ordinate directions and energies independently of all other domains, potentially allowing for much better scaling than possible with full sweeps. The PBJ algorithm has been implemented in NEWTRNX using a Gauss-Seidel iteration in energy and an asynchronous communication by an energy group, such that each partition utilizes the latest boundary solution available for each group before solving the withingroup scattering in a given group. For each energy group, the within-group scattering converges with a generalized minimum residual (GMRES) solver, preconditioned with beta transport synthetic acceleration ({beta}-TSA).

- Authors:

- ORNL

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 958802

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Conference

- Resource Relation:
- Conference: ANS2007 Winter Meeting, Washington, DC, USA, 20071111, 20071115

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ACCELERATION; ALGORITHMS; COMMUNICATIONS; COMPUTERS; DISCRETE ORDINATE METHOD; IMPLEMENTATION; REACTORS; SCATTERING; TRANSPORT

### Citation Formats

```
Clarno, Kevin T.
```*Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport*. United States: N. p., 2007.
Web.

```
Clarno, Kevin T.
```*Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport*. United States.

```
Clarno, Kevin T. Mon .
"Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport". United States.
doi:.
```

```
@article{osti_958802,
```

title = {Implementation of Generalized Coarse-Mesh Rebalance of NEWTRNX for Acceleration of Parallel Block-Jacobi Transport},

author = {Clarno, Kevin T},

abstractNote = {The NEWTRNX transport module solves the multigroup, discrete-ordinates source-driven or k-eigenvalue transport equation in parallel on a 3-D unstructured tetrahedral mesh using the extended step characteristics (ESC), also known as the slice-balance approach (SBA), spatial discretization. The spatial domains are decomposed using METIS. NEWTRNX is under development for nuclear reactor analysis on computer hardware ranging from clusters to massively parallel machines, like the Cray XT4. Transport methods that rely on full sweeps across the spatial domain have been shown to display poor scaling for thousands of processors. The Parallel Block-Jacobi (PBJ) algorithm allows each spatial partition to sweep over all discrete-ordinate directions and energies independently of all other domains, potentially allowing for much better scaling than possible with full sweeps. The PBJ algorithm has been implemented in NEWTRNX using a Gauss-Seidel iteration in energy and an asynchronous communication by an energy group, such that each partition utilizes the latest boundary solution available for each group before solving the withingroup scattering in a given group. For each energy group, the within-group scattering converges with a generalized minimum residual (GMRES) solver, preconditioned with beta transport synthetic acceleration ({beta}-TSA).},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Jan 01 00:00:00 EST 2007},

month = {Mon Jan 01 00:00:00 EST 2007}

}