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 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.

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.