A parallel method for solving pentadiagonal systems of linear equations

A new parallel approach for solving a pentadiagonal linear system is presented. The parallel partition method for this system and the TW parallel partition method on a chain of P processors are introduced and discussed. The result of this algorithm is a reduced pentadiagonal linear system of order P \Gamma 2 compared with a system of order 2P \Gamma 2 for the parallel partition method. More importantly the new method involves only half the number of communications startups than the parallel partition method (and other standard parallel methods) and hence is a far more efficient parallel algorithm.

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.

Intelligent Systems and Soft Computing for Nuclear Science and Industry, Proc. 2nd Int. FLINS Workshop, ed. D. Ruan & al., World Scientific, 1996 [Book review]

Abstract not available