Parallel dynamic graph-partitioning for unstructured meshes

A parallel method for the dynamic partitioning of unstructured meshes is described. The method introduces a new iterative optimization technique known as relative gain optimization which both balances the workload and attempts to minimize the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.

Multilevel mesh partitioning for optimizing domain shape

Multilevel algorithms are a successful class of optimization techniques that address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimization method that refines the partition at each graph level. To date, these algorithms have been used almost exclusively to minimize the cut-edge weight in the graph with the aim of minimizing the parallel communication overhead. However, it has been shown that for certain classes of problems, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. Therefore, in this paper, the authors modify the multilevel algorithms to optimize a cost function based on the aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Multilevel mesh partitioning for heterogeneous communication networks

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut edge weight in the graph with the aim of minimising the parallel communication overhead, but recently there has been a perceived need to take into account the communications network of the parallel machine. For example the increasing use of SMP clusters (systems of multiprocessor compute nodes with very fast intra-node communications but relatively slow inter-node networks) suggest the use of hierarchical network models. Indeed this requirement is exacerbated in the early experiments with meta-computers (multiple supercomputers combined together, in extreme cases over inter-continental networks). In this paper therefore, we modify a multilevel algorithm in order to minimise a cost function based on a model of the communications network. Several network models and variants of the algorithm are tested and we establish that it is possible to successfully guide the optimisation to reflect the chosen architecture.

Multilevel mesh partitioning for optimising domain shape

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Evaluation of the JOSTLE mesh partitioning code for practical multiphysics applications

The use of unstructured mesh codes on parallel machines is one of the most effective ways to solve large computational mechanics problems. Completely general geometries and complex behaviour can be modelled and, in principle, the inherent sparsity of many such problems can be exploited to obtain excellent parallel efficiencies. However, unlike their structured counterparts, the problem of distributing the mesh across the memory of the machine, whilst minimising the amount of interprocessor communication, must be carefully addressed. This process is an overhead that is not incurred by a serial code, but is shown to rapidly computable at turn time and tailored for the machine being used.

Load-balancing for parallel adaptive unstructured grids

A parallel method for the dynamic partitioning of unstructured meshes is outlined. The method includes diffusive load-balancing techniques and an iterative optimisation technique known as relative gain optimisationwhich both balances theworkload and attempts to minimise the interprocessor communications overhead. It can also optionally include amultilevel strategy. Experiments on a series of adaptively refined meshes indicate that the algorithmprovides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.

Parallel dynamic load-balancing for adaptive unstructured meshes

This chapter describes a parallel optimization technique that incorporates a distributed load-balancing algorithm and provides an extremely fast solution to the problem of load-balancing adaptive unstructured meshes. Moreover, a parallel graph contraction technique can be employed to enhance the partition quality and the resulting strategy outperforms or matches results from existing state-of-the-art static mesh partitioning algorithms. The strategy can also be applied to static partitioning problems. Dynamic procedures have been found to be much faster than static techniques, to provide partitions of similar or higher quality and, in comparison, involve the migration of a fraction of the data. The method employs a new iterative optimization technique that balances the workload and attempts to minimize the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more quickly. The dynamic evolution of load has three major influences on possible partitioning techniques; cost, reuse, and parallelism. The unstructured mesh may be modified every few time-steps and so the load-balancing must have a low cost relative to that of the solution algorithm in between remeshing.

Dynamic load-balancing for parallel adaptive unstructured meshes

A parallel method for dynamic partitioning of unstructured meshes is described. The method employs a new iterative optimisation technique which both balances the workload and attempts to minimise the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more quickly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.

Multilevel mesh partitioning for optimising subdomain aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight in the graph with the aim of minimising the parallel communication overhead. However it has been shown that for certain classes of problem, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Parallel dynamic graph-partitioning for unstructured meshes

A parallel method for the dynamic partitioning of unstructured meshes is described. The method introduces a new iterative optimisation technique known as relative gain optimisation which both balances the workload and attempts to minimise the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.