# Parallel Optimisation Algorithms

for Multilevel Mesh Partitioning

**
C. Walshaw and M. Cross
**

### Abstract:

Three parallel optimisation algorithms, for use in the context of multilevel graph partitioning of unstructured meshes, are described.
The first, interface optimisation, reduces the computation to a set of independent optimisation problems in interface regions.
The next, alternating optimisation, is a restriction of this technique in which mesh entities are only allowed to migrate between subdomains in one direction.
The third treats the gain as a potential field and uses the concept of relative gain for selecting appropriate vertices to migrate.
The results are compared and seen to produce very high global quality partitions, very rapidly.
The results are also compared with another partitioning tool and shown to be of higher quality although taking longer to compute.

**Key words.**
mesh partitioning, load-balancing, multilevel algorithms.

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Fri Aug 13 13:40:22 BST 2004