# Reducing Communication in Algebraic Multigrid Using Additive Variants

## Abstract

Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1237550

- Report Number(s):
- LLNL-JRNL-637872

Journal ID: ISSN 1070-5325

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Numerical Linear Algebra with Applications

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 1; Journal ID: ISSN 1070-5325

- Publisher:
- Wiley

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

### Citation Formats

```
Vassilevski, Panayot S., and Yang, Ulrike Meier.
```*Reducing Communication in Algebraic Multigrid Using Additive Variants*. United States: N. p., 2014.
Web. doi:10.1002/nla.1928.

```
Vassilevski, Panayot S., & Yang, Ulrike Meier.
```*Reducing Communication in Algebraic Multigrid Using Additive Variants*. United States. doi:10.1002/nla.1928.

```
Vassilevski, Panayot S., and Yang, Ulrike Meier. Wed .
"Reducing Communication in Algebraic Multigrid Using Additive Variants". United States. doi:10.1002/nla.1928. https://www.osti.gov/servlets/purl/1237550.
```

```
@article{osti_1237550,
```

title = {Reducing Communication in Algebraic Multigrid Using Additive Variants},

author = {Vassilevski, Panayot S. and Yang, Ulrike Meier},

abstractNote = {Algebraic multigrid (AMG) has proven to be an effective scalable solver on many high performance computers. However, its increasing communication complexity on coarser levels has shown to seriously impact its performance on computers with high communication cost. Moreover, additive AMG variants provide not only increased parallelism as well as decreased numbers of messages per cycle but also generally exhibit slower convergence. Here we present various new additive variants with convergence rates that are significantly improved compared to the classical additive algebraic multigrid method and investigate their potential for decreased communication, and improved communication-computation overlap, features that are essential for good performance on future exascale architectures.},

doi = {10.1002/nla.1928},

journal = {Numerical Linear Algebra with Applications},

issn = {1070-5325},

number = 1,

volume = 21,

place = {United States},

year = {2014},

month = {2}

}

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