# Matrix substructuring, domain decomposition, and particle methods: Current trends for solving PDE's (partial differential equations) in parallel

## Abstract

This paper discusses some of the directions being taken in the development of numerical algorithms that can be efficiently executed on vector and parallel computers. Heretofore, most of the research has been on developing parallel algorithms for solving a linear system of equations. A summary is given for the general approach taken by many of the algorithms. Realizing that the brief description does not do justice to many of the algorithms that have been devised, an extensive reference list is given. Two approaches are discussed that will have an important impact on the development of parallel algorithms. Each are motivated from the assumption that the most effective way for obtaining parallelism is to approach the scientific problem in a different manner. A technique that has been labeled domain decomposition is studied. The basic idea is that the scientific problem is not modeled by single mathematical model but rather as a collection of mathematical models that are coupled to one-another through the spatial domain of influence of the global physical problem. New directions in particle methods are studied. In this section, the idea of viewing the physical world as particles instead of continuum is resurrected. However, in this section the authorsmore »

- Authors:

- Publication Date:

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

- OSTI Identifier:
- 5090976

- Report Number(s):
- UCRL-98663; CONF-8804118-1

ON: DE88009826

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: IEE workshop on design and application of parallel digital processors, Lisbon, Portugal, 11 Apr 1988

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARALLEL PROCESSING; VECTOR PROCESSING; MATHEMATICAL MODELS; PROGRAMMING; 990210* - Supercomputers- (1987-1989)

### Citation Formats

```
Elton, B, Perkins, A L, and Rodrigue, G.
```*Matrix substructuring, domain decomposition, and particle methods: Current trends for solving PDE's (partial differential equations) in parallel*. United States: N. p., 1988.
Web.

```
Elton, B, Perkins, A L, & Rodrigue, G.
```*Matrix substructuring, domain decomposition, and particle methods: Current trends for solving PDE's (partial differential equations) in parallel*. United States.

```
Elton, B, Perkins, A L, and Rodrigue, G. 1988.
"Matrix substructuring, domain decomposition, and particle methods: Current trends for solving PDE's (partial differential equations) in parallel". United States.
```

```
@article{osti_5090976,
```

title = {Matrix substructuring, domain decomposition, and particle methods: Current trends for solving PDE's (partial differential equations) in parallel},

author = {Elton, B and Perkins, A L and Rodrigue, G},

abstractNote = {This paper discusses some of the directions being taken in the development of numerical algorithms that can be efficiently executed on vector and parallel computers. Heretofore, most of the research has been on developing parallel algorithms for solving a linear system of equations. A summary is given for the general approach taken by many of the algorithms. Realizing that the brief description does not do justice to many of the algorithms that have been devised, an extensive reference list is given. Two approaches are discussed that will have an important impact on the development of parallel algorithms. Each are motivated from the assumption that the most effective way for obtaining parallelism is to approach the scientific problem in a different manner. A technique that has been labeled domain decomposition is studied. The basic idea is that the scientific problem is not modeled by single mathematical model but rather as a collection of mathematical models that are coupled to one-another through the spatial domain of influence of the global physical problem. New directions in particle methods are studied. In this section, the idea of viewing the physical world as particles instead of continuum is resurrected. However, in this section the authors discuss how new particle methods have been developed that can be effectively used on parallel computers.},

doi = {},

url = {https://www.osti.gov/biblio/5090976},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1988},

month = {4}

}