A generic strategy for dynamic load balancing of distributed memory parallel computational mechanics using unstructured meshes

A large class of computational problems are characterised by frequent synchronisation, and computational requirements which change as a function of time. When such a problem is solved on a message passing multiprocessor machine [5], the combination of these characteristics leads to system performance which deteriorate in time. As the communication performance of parallel hardware steadily improves so load balance becomes a dominant factor in obtaining high parallel efficiency. Performance can be improved with periodic redistribution of computational load; however, redistribution can sometimes be very costly. We study the issue of deciding when to invoke a global load re-balancing mechanism. Such a decision policy must actively weigh the costs of remapping against the performance benefits, and should be general enough to apply automatically to a wide range of computations. This paper discusses a generic strategy for Dynamic Load Balancing (DLB) in unstructured mesh computational mechanics applications. The strategy is intended to handle varying levels of load changes throughout the run. The major issues involved in a generic dynamic load balancing scheme will be investigated together with techniques to automate the implementation of a dynamic load balancing mechanism within the Computer Aided Parallelisation Tools (CAPTools) environment, which is a semi-automatic tool for parallelisation of mesh based FORTRAN codes.

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.

Load balancing for aspect ratio in adaptive finite element simulations

In parallel adaptive finite element simulations the work load on the individual processors may change frequently. To (re)distribute the load evenly over the processors a load balancing heuristic is needed. Common strategies try to minimise subdomain dependencies by optimising the cutsize of the partitioning. However for certain solvers cutsize only plays a minor role, and their convergence is highly dependent on the subdomain shapes. Degenerated subdomain shapes cause them to need significantly more iterations to converge. In this work a new parallel load balancing strategy is introduced which directly addresses the problem of generating and conserving reasonably good subdomain shapes in a dynamically changing Finite Element Simulation. Geometric data is used to formulate several cost functions to rate elements in terms of their suitability to be migrated. The well known diffusive method which calculates the necessary load flow is enhanced by weighting the subdomain edges with the help of these cost functions. The proposed methods have been tested and results are presented.

Load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It calculates a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-of-the-art balancers show the benefits of the construction.

Dynamic load balancing of distributed memory parallel computational mechanics using unstructured meshes for multi-physical modelling

As the complexity of parallel applications increase, the performance limitations resulting from computational load imbalance become dominant. Mapping the problem space to the processors in a parallel machine in a manner that balances the workload of each processors will typically reduce the run-time. In many cases the computation time required for a given calculation cannot be predetermined even at run-time and so static partition of the problem returns poor performance. For problems in which the computational load across the discretisation is dynamic and inhomogeneous, for example multi-physics problems involving fluid and solid mechanics with phase changes, the workload for a static subdomain will change over the course of a computation and cannot be estimated beforehand. For such applications the mapping of loads to process is required to change dynamically, at run-time in order to maintain reasonable efficiency. The issue of dynamic load balancing are examined in the context of PHYSICA, a three dimensional unstructured mesh multi-physics continuum mechanics computational modelling code.

Mesh partitioning and load balancing for distributed memory parallel systems

A method is outlined for optimising graph partitions which arise in mapping unstructured mesh calculations to parallel computers. The method employs a relative gain iterative technique to both evenly balance the workload and minimise the number and volume of interprocessor communications. A parallel graph reduction technique is also briefly described and can be used to give a global perspective to the optimisation. The algorithms work efficiently in parallel as well as sequentially and when combined with a fast direct partitioning technique (such as the Greedy algorithm) to give an initial partition, the resulting two-stage process proves itself to be both a powerful and flexible solution to the static graph-partitioning problem. Experiments indicate that the resulting parallel code can provide high quality partitions, independent of the initial partition, within a few seconds. The algorithms can also be used for dynamic load-balancing, reusing existing partitions and in this case the procedures are much faster than static techniques, provide partitions of similar or higher quality and, in comparison, involve the migration of a fraction of the data.

Automatic implementation of dynamic load balancing strategies for structured computational mechanics codes

This paper presents a new dynamic load balancing technique for structured mesh computational mechanics codes in which the processor partition range limits of just one of the partitioned dimensions uses non-coincidental limits, as opposed to using coincidental limits in all of the partitioned dimensions. The partition range limits are 'staggered', allowing greater flexibility in obtaining a balanced load distribution in comparison to when the limits are changed 'globally'. as the load increase/decrease on one processor no longer restricts the load decrease/increase on a neighbouring processor. The automatic implementation of this 'staggered' load balancing strategy within an existing parallel code is presented in this paper, along with some preliminary results.