# A parallel multigrid method for solving elliptic partial differential equations

## Abstract

This paper introduces a parallel multigrid method for solving elliptic partial differential equations. This method combines two other methods, both of which are popular methods under research today. One of the methods is a multigrid method, essentially a sequential method. The other is a parallel domain decomposition method, a variation on the Schwarz alternating procedure. Each method is explained individually, before the combined method is explained. The combined method is then compared to each of the individual methods, demonstrating the superiority of the combined method over each of its parent methods. As a model problem Poisson's equation is used. The computer on which the various methods were tested is an Alliant FX/8, a shared memory multiprocessor machine having 8 processors which can be run simultaneously is executing parallel code. 19 refs.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- DOE/ER

- OSTI Identifier:
- 7055158

- Report Number(s):
- UCRL-53918

ON: DE90007929

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

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Thesis (M.S.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARTIAL DIFFERENTIAL EQUATIONS; PARALLEL PROCESSING; ALGORITHMS; ARRAY PROCESSORS; BOUNDARY-VALUE PROBLEMS; CONVERGENCE; ELLIPTICAL CONFIGURATION; ITERATIVE METHODS; NUMERICAL SOLUTION; CONFIGURATION; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL LOGIC; PROGRAMMING; 990200* - Mathematics & Computers

### Citation Formats

```
Ferretta, T. E.
```*A parallel multigrid method for solving elliptic partial differential equations*. United States: N. p., 1989.
Web. doi:10.2172/7055158.

```
Ferretta, T. E.
```*A parallel multigrid method for solving elliptic partial differential equations*. United States. https://doi.org/10.2172/7055158

```
Ferretta, T. E. 1989.
"A parallel multigrid method for solving elliptic partial differential equations". United States. https://doi.org/10.2172/7055158. https://www.osti.gov/servlets/purl/7055158.
```

```
@article{osti_7055158,
```

title = {A parallel multigrid method for solving elliptic partial differential equations},

author = {Ferretta, T. E.},

abstractNote = {This paper introduces a parallel multigrid method for solving elliptic partial differential equations. This method combines two other methods, both of which are popular methods under research today. One of the methods is a multigrid method, essentially a sequential method. The other is a parallel domain decomposition method, a variation on the Schwarz alternating procedure. Each method is explained individually, before the combined method is explained. The combined method is then compared to each of the individual methods, demonstrating the superiority of the combined method over each of its parent methods. As a model problem Poisson's equation is used. The computer on which the various methods were tested is an Alliant FX/8, a shared memory multiprocessor machine having 8 processors which can be run simultaneously is executing parallel code. 19 refs.},

doi = {10.2172/7055158},

url = {https://www.osti.gov/biblio/7055158},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1989},

month = {2}

}