# An overlapping domain decomposition method for large-scale problems

## Abstract

Discretization of dynamical models defined through partial differential equations leads to large-scale systems. Time-depending condition involves an iterative integration of such kind of systems. In this paper, a novel technique based on overlapped domain decomposition, without preconditioner and scalable, is presented. Due to the domain decomposition, subproblems are solved in parallel without communications, cutting off the computation time and optimizing the computational cost. This direct method describes an optimized parallel strategy to solve the initial problem, providing the exact solution, up to rounding errors. Moreover, it takes into account both physical nature of the problem and deriving numerical properties of the system. It is highly recommended in case of band matrices and a long time interval because of an increasing gain in terms of performance and computational cost with the number of integrations. A deep analysis of the computational cost concludes the paper.

- Authors:

- Messina University, Department of Mathematical and Computer Sciences, Physical Sciences, and Earth Sciences (Italy)
- University of Enna Kore, Faculty of Engineering and Architecture (Italy)

- Publication Date:

- OSTI Identifier:
- 22769262

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; ERRORS; EXACT SOLUTIONS; MATRICES; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS

### Citation Formats

```
Agreste, Santa, and Ricciardello, Angela.
```*An overlapping domain decomposition method for large-scale problems*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0541-Y.

```
Agreste, Santa, & Ricciardello, Angela.
```*An overlapping domain decomposition method for large-scale problems*. United States. doi:10.1007/S40314-017-0541-Y.

```
Agreste, Santa, and Ricciardello, Angela. Sun .
"An overlapping domain decomposition method for large-scale problems". United States. doi:10.1007/S40314-017-0541-Y.
```

```
@article{osti_22769262,
```

title = {An overlapping domain decomposition method for large-scale problems},

author = {Agreste, Santa and Ricciardello, Angela},

abstractNote = {Discretization of dynamical models defined through partial differential equations leads to large-scale systems. Time-depending condition involves an iterative integration of such kind of systems. In this paper, a novel technique based on overlapped domain decomposition, without preconditioner and scalable, is presented. Due to the domain decomposition, subproblems are solved in parallel without communications, cutting off the computation time and optimizing the computational cost. This direct method describes an optimized parallel strategy to solve the initial problem, providing the exact solution, up to rounding errors. Moreover, it takes into account both physical nature of the problem and deriving numerical properties of the system. It is highly recommended in case of band matrices and a long time interval because of an increasing gain in terms of performance and computational cost with the number of integrations. A deep analysis of the computational cost concludes the paper.},

doi = {10.1007/S40314-017-0541-Y},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}