# A parallel version of a multigrid algorithm for isotropic transport equations

## Abstract

The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a finite element method called the modified linear discontinuous (MLD) scheme. The MLD scheme represents a lumped version of the standard linear discontinuous (LD) scheme. The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown.

- Authors:

- (Univ. of Colorado, Boulder, CO (United States). Program in Applied Mathematics)
- (Los Alamos National Lab., NM (United States). Computer Research Group)

- Publication Date:

- OSTI Identifier:
- 5008876

- DOE Contract Number:
- FG02-90ER25086

- Resource Type:
- Journal Article

- Journal Name:
- SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States)

- Additional Journal Information:
- Journal Volume: 15:2; Journal ID: ISSN 0196-5204

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NEUTRON DIFFUSION EQUATION; ALGORITHMS; FINITE ELEMENT METHOD; PARALLEL PROCESSING; SLABS; SUPERCOMPUTERS; CALCULATION METHODS; COMPUTERS; DIFFERENTIAL EQUATIONS; DIGITAL COMPUTERS; EQUATIONS; MATHEMATICAL LOGIC; NUMERICAL SOLUTION; PROGRAMMING; 663610* - Neutron Physics- (1992-); 990200 - Mathematics & Computers

### Citation Formats

```
Manteuffel, T., McCormick, S., Yang, G., Morel, J., and Oliveira, S.
```*A parallel version of a multigrid algorithm for isotropic transport equations*. United States: N. p., 1994.
Web. doi:10.1137/0915032.

```
Manteuffel, T., McCormick, S., Yang, G., Morel, J., & Oliveira, S.
```*A parallel version of a multigrid algorithm for isotropic transport equations*. United States. doi:10.1137/0915032.

```
Manteuffel, T., McCormick, S., Yang, G., Morel, J., and Oliveira, S. Tue .
"A parallel version of a multigrid algorithm for isotropic transport equations". United States. doi:10.1137/0915032.
```

```
@article{osti_5008876,
```

title = {A parallel version of a multigrid algorithm for isotropic transport equations},

author = {Manteuffel, T. and McCormick, S. and Yang, G. and Morel, J. and Oliveira, S.},

abstractNote = {The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a finite element method called the modified linear discontinuous (MLD) scheme. The MLD scheme represents a lumped version of the standard linear discontinuous (LD) scheme. The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown.},

doi = {10.1137/0915032},

journal = {SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States)},

issn = {0196-5204},

number = ,

volume = 15:2,

place = {United States},

year = {1994},

month = {3}

}

DOI: 10.1137/0915032

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