# Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems

## Abstract

Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned asmore »

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 15005342

- Report Number(s):
- UCRL-JC-147742

TRN: US200322%%382

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: International Conference on Computational Engineering and Sciences, Reno, NV (US), 07/31/2002--08/02/2002; Other Information: PBD: 21 Mar 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 33 ADVANCED PROPULSION SYSTEMS; 42 ENGINEERING; ALGORITHMS; DEFORMATION; GEOMETRY; IMPLEMENTATION; ORIGIN; PERFORMANCE; ROCKETS

### Citation Formats

```
Crane, N K, Parsons, I D, and Hjelmstad, K D.
```*Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems*. United States: N. p., 2002.
Web.

```
Crane, N K, Parsons, I D, & Hjelmstad, K D.
```*Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems*. United States.

```
Crane, N K, Parsons, I D, and Hjelmstad, K D. 2002.
"Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems". United States. https://www.osti.gov/servlets/purl/15005342.
```

```
@article{osti_15005342,
```

title = {Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems},

author = {Crane, N K and Parsons, I D and Hjelmstad, K D},

abstractNote = {Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.},

doi = {},

url = {https://www.osti.gov/biblio/15005342},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2002},

month = {3}

}