# On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations

## Abstract

The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observed to be less effective in higher dimensions. This is due in part to the expense of solving the related diffusion linear system. We investigate here the effectiveness of a parallel semicoarsening multigrid (SMG) solution approach to DSA preconditioning in several three dimensional problems. In particular, we consider the algorithmic and implementation scalability of a parallel SMG-DSA preconditioner on several types of test problems.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 2775

- Report Number(s):
- UCRL-JC-130877; YN0100000

YN0100000; TRN: US0101314

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Conference

- Resource Relation:
- Conference: Super Computing 98, Orlando, FL (US), 11/07/1998--11/13/1998; Other Information: PBD: 14 May 1998

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; BOLTZMANN EQUATION; CHARGED-PARTICLE TRANSPORT; INTEGRO-DIFFERENTIAL EQUATIONS; NEUTRAL-PARTICLE TRANSPORT; ITERATIVE METHODS

### Citation Formats

```
Brown, P, and Chang, B.
```*On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations*. United States: N. p., 1998.
Web.

```
Brown, P, & Chang, B.
```*On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations*. United States.

```
Brown, P, and Chang, B. Thu .
"On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations". United States. https://www.osti.gov/servlets/purl/2775.
```

```
@article{osti_2775,
```

title = {On the use of diffusion synthetic acceleration in parallel 3D neutral particle transport calculations},

author = {Brown, P and Chang, B},

abstractNote = {The linear Boltzmann transport equation (BTE) is an integro-differential equation arising in deterministic models of neutral and charged particle transport. In slab (one-dimensional Cartesian) geometry and certain higher-dimensional cases, Diffusion Synthetic Acceleration (DSA) is known to be an effective algorithm for the iterative solution of the discretized BTE. Fourier and asymptotic analyses have been applied to various idealizations (e.g., problems on infinite domains with constant coefficients) to obtain sharp bounds on the convergence rate of DSA in such cases. While DSA has been shown to be a highly effective acceleration (or preconditioning) technique in one-dimensional problems, it has been observed to be less effective in higher dimensions. This is due in part to the expense of solving the related diffusion linear system. We investigate here the effectiveness of a parallel semicoarsening multigrid (SMG) solution approach to DSA preconditioning in several three dimensional problems. In particular, we consider the algorithmic and implementation scalability of a parallel SMG-DSA preconditioner on several types of test problems.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1998},

month = {5}

}