# A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

## Abstract

Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22382168

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DIAGRAMS; FLUID MECHANICS; INDICATORS; LOCALITY; MAPPING; METRICS; PARTITION; PERFORMANCE; SPACE

### Citation Formats

```
Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca, Salehi, M. Mahdi, and Bushe, W. Kendal.
```*A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.10.022.

```
Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca, Salehi, M. Mahdi, & Bushe, W. Kendal.
```*A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries*. United States. doi:10.1016/J.JCP.2014.10.022.

```
Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca, Salehi, M. Mahdi, and Bushe, W. Kendal. Thu .
"A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries". United States.
doi:10.1016/J.JCP.2014.10.022.
```

```
@article{osti_22382168,
```

title = {A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries},

author = {Nivarti, Girish V., E-mail: g.nivarti@alumni.ubc.ca and Salehi, M. Mahdi and Bushe, W. Kendal},

abstractNote = {Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.},

doi = {10.1016/J.JCP.2014.10.022},

journal = {Journal of Computational Physics},

number = ,

volume = 281,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}