this paper we describe such a parallel optimization technique

We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diffusion type. Within this framework we develop a new optimal polynomial scheme (OPS) which we show to terminate within a finite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all existing diffusion load balancing algorithms, including OPS, determine a flow of load on the edges of the graph which is uniquely defined, independent of the method and minimal in the l 2 -norm. This result can be extended to edge weighted graphs. The l 2 -minimality is achieved only if a diffusion algorithm is used as preprocessing and the real movement of load is performed in a second step. Thus, it is advisable to split the balancing process into the two steps of first determining a balancing flow and afterwards moving the load. We introduce the problem of scheduling a flow and present some first results on its complexity and the ...

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. 2000 Elsevier Science B.V. All rights reserved.

. In many important computational mechanics applications, the computation adapts dynamically during the simulation. Examples include adaptive mesh refinement, particle simulations and transient dynamics calculations. When running these kinds of simulations on a parallel computer, the work must be assigned to processors in a dynamic fashion to keep the computational load balanced. A number of approaches have been proposed for this dynamic load balancing problem. This paper reviews the major classes of algorithms, and discusses their relative merits on problems from computational mechanics. Shortcomings in the state-of-the-art are identified and suggestions are made for future research directions. Key words. dynamic load balancing, parallel computer, adaptive mesh refinement 1. Introduction. The efficient use of a parallel computer requires two, often competing, objectives to be achieved. First, the processors must be kept busy doing useful work. And second, the amount of interprocess...

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. Key words. graph-partitioning, adaptive unstructured meshes, load-balancing, parallel scientific computation. 1 Introduction The use of unstructured mesh codes on parallel machines can be one of the most efficient ways to solve large Computational Fluid Dynamics (CFD) and Computational Mechanics (CM) problems. Completely general geometries and complex behaviour can be readily modelled an...

Load balancing in large parallel systems with distributed memory is a difficult task often influencing the overall efficiency of applications substantially. A number of efficient distributed load balancing strategies have been developed in the recent years. Although they are currently not generally available as part of parallel operating systems, it is often not difficult to integrate them into applications. This paper gives a classification of different load balancing problems based on application characteristics. For the case of applications out of the field of scientific computing, useful methods are described in more detail.

The Paderborn University BSP (PUB) library is a parallel C library based on the BSP model. The basic library supports buffered and unbuffered asynchronous communication between any pair of processors, and a mechanism for synchronizing the processors in a barrier style. In addition, it provides routines for collective communication on arbitrary subsets of processors, partition operations, and a zero-cost synchronization mechanism. Furthermore, some techniques used in its implementation deviate significantly from the techniques used in other BSP libraries. 1. Introduction Most message-passing libraries, like PVM[6] and MPI[12], are based on pairwise sends and receives. This means that for each send operation, a matching receive has to be issued on the destination processor. This approach, however, is very error prone because deadlocks can be easily introduced if a message is never accepted. Furthermore, it is difficult to determine the correctness and complexity of programs implemented ...

With nearest neighbor load balancing algorithms, a processor makes balancing decisions based on localized workload information and manages workload migrations within its neighborhood. This paper compares a couple of fairly well-known nearest neighbor algorithms, the dimension-exchange (DE, for short) and the diffusion (DF, for short) methods and their several variants---the average dimension-exchange (ADE), the optimally-tuned dimension-exchange (ODE), the local average diffusion (ADF) and the optimally-tuned diffusion (ODF). The measures of interest are their efficiency in driving any initial workload distribution to a uniform distribution and their ability in controlling the growth of the variance among the processors' workloads. The comparison is made with respect to both one-port and all-port communication architectures and in consideration of various implementation strategies including synchronous/asynchronous invocation policies and static/dynamic random workload behaviors. It t...

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. 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 solution algorithm, the convergence of the solver is strongly influenced 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. Keywords: graph-partitioning, mesh-partitioning, multilevel algorithms, aspect ratio, domain decomposition preconditioning. 1 Introduction The need for mesh partitioning arises naturally in many f...

A parallel method for dynamic partitioning of unstructured meshes is described. The method employs a new unified 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 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. Key words. graph-partitioning, unstructured meshes, dynamic load-balancing. 1 Introduction The use of unstructured mesh codes on parallel machines can be one of the most efficient ways to solve large Computational Fluid Dynamics (CFD) and Computational Mechanics (CM) problems. Completely general geometries and complex behaviour can be readily modelled and, in principle, the inherent sparsit...