# CMFD and coarse-mesh DSA

## Abstract

The Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are two widely-used, independently-developed acceleration methods for iteratively solving deterministic particle transport simulations. In this paper we show that these methods are related in the following way: if the standard notion of DSA as a 'fine mesh' method is generalized to that of a coarse mesh method, then the linearized form of CMFD is algebraically equivalent to a coarse mesh form of DSA. Also, we demonstrate theoretically (via Fourier analysis) and computationally that CMFD and coarse mesh DSA have nearly the same convergence properties. (authors)

- Authors:

- Dept. of Nuclear Engineering and Radiological Sciences, Univ. of Michigan, Ann Arbor, MI 48109-2104 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

- OSTI Identifier:
- 22105622

- Resource Type:
- Conference

- Resource Relation:
- Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 14 refs.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; CONVERGENCE; DIFFUSION; FINITE DIFFERENCE METHOD; FOURIER ANALYSIS; PARTICLES; TRANSPORT THEORY

### Citation Formats

```
Larsen, E. W., and Kelley, B. W.
```*CMFD and coarse-mesh DSA*. United States: N. p., 2012.
Web.

```
Larsen, E. W., & Kelley, B. W.
```*CMFD and coarse-mesh DSA*. United States.

```
Larsen, E. W., and Kelley, B. W. Sun .
"CMFD and coarse-mesh DSA". United States.
```

```
@article{osti_22105622,
```

title = {CMFD and coarse-mesh DSA},

author = {Larsen, E. W. and Kelley, B. W.},

abstractNote = {The Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are two widely-used, independently-developed acceleration methods for iteratively solving deterministic particle transport simulations. In this paper we show that these methods are related in the following way: if the standard notion of DSA as a 'fine mesh' method is generalized to that of a coarse mesh method, then the linearized form of CMFD is algebraically equivalent to a coarse mesh form of DSA. Also, we demonstrate theoretically (via Fourier analysis) and computationally that CMFD and coarse mesh DSA have nearly the same convergence properties. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {7}

}

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