A Three-Level Parallelisation Scheme and Application to the Nelder-Mead Algorithm
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We consider a three-level parallelisation scheme. The second and third levels define a classical two-level parallelisation scheme and some load balancing algorithm is used to distribute tasks among processes. It is well-known that for many applications the efficiency of parallel algorithms of the second and third level starts to drop down after some critical parallelisation degree is reached. This weakness of the two-level template is addressed by introduction of one additional parallelisation level. As an alternative to the basic solver some new or modified algorithm is considered on this level. The idea of the proposed methodology is to choose the compromise between increasing the parallelisation degree but using less efficient algorithm in comparison with the best sequential solver. As an example we investigate two modified simplex downhill methods. On the second level a set of partial differential equations are solved numerically and on the third level the parallel Wang's algorithm is used to solve systems of linear equations with tridiagonal matrices. A greedy workload balancing heuristic is proposed, which is oriented to the case of a large number of available processors.
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