# Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems

## Abstract

Algebraic multigrid (AMG) is an attractive choice for solving large linear systems {Lambda}x = b on unstructured grids. While AMG is applicable as a solver for a variety of problems, its robustness may be enhanced by using it as a preconditioner for Krylov solvers, such as GMRES. The sheer size of modern problems, hundreds of millions or billions of unknowns, dictates the use of massively parallel computers. AMG consists of two phases: the setup phase, in which smaller and smaller linear systems are generated by means of linear transfer operators (interpolation and restriction); and the solve phase, which employs a smoothing operator, such as Gauss-Seidel or Jacobi relaxation. Most of these components can be parallelized in a straightforward fashion; however, the coarse-grid selection, in which the grid for a smaller linear system is created on which the error can be approximated, is highly sequential. It is important to develop parallel coarsening techniques. They briefly present here the coarsening algorithms used in the parallel AMG code ''Boomer AMG'' and summarize some performance results for those algorithms. A detailed discussion of the algorithms and numerical results will be found.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 15006488

- Report Number(s):
- UCRL-JC-136477

TRN: US200411%%229

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: 16th International Association for Mathematics and Computers in Simulation World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation, Lausanne (CH), 08/21/2000--08/25/2000; Other Information: PBD: 22 Feb 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ALGORITHMS; COMPUTERS; INTERPOLATION; PERFORMANCE; RELAXATION; SIMULATION

### Citation Formats

```
Hensor, V E, and Yang, U M.
```*Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems*. United States: N. p., 2000.
Web.

```
Hensor, V E, & Yang, U M.
```*Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems*. United States.

```
Hensor, V E, and Yang, U M. Tue .
"Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems". United States. https://www.osti.gov/servlets/purl/15006488.
```

```
@article{osti_15006488,
```

title = {Experiences with BoomerAMG:: A Parallel Algebraic Multigrid Solver and Preconditioner for Large Linear Systems},

author = {Hensor, V E and Yang, U M},

abstractNote = {Algebraic multigrid (AMG) is an attractive choice for solving large linear systems {Lambda}x = b on unstructured grids. While AMG is applicable as a solver for a variety of problems, its robustness may be enhanced by using it as a preconditioner for Krylov solvers, such as GMRES. The sheer size of modern problems, hundreds of millions or billions of unknowns, dictates the use of massively parallel computers. AMG consists of two phases: the setup phase, in which smaller and smaller linear systems are generated by means of linear transfer operators (interpolation and restriction); and the solve phase, which employs a smoothing operator, such as Gauss-Seidel or Jacobi relaxation. Most of these components can be parallelized in a straightforward fashion; however, the coarse-grid selection, in which the grid for a smaller linear system is created on which the error can be approximated, is highly sequential. It is important to develop parallel coarsening techniques. They briefly present here the coarsening algorithms used in the parallel AMG code ''Boomer AMG'' and summarize some performance results for those algorithms. A detailed discussion of the algorithms and numerical results will be found.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {2}

}