Abstract
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 these two levels starts to drop down after some critical parallelisation degree is reached. This weakness of the twolevel template is addressed by introduction of one additional parallelisation level. s an alternative to the basic solver some new or modified algorithms are considered on this level. The idea of the proposed methodology is to increase the parallelisation degree by using possibly less efficient algorithms in comparison with the basic solver. As an example we investigate two modified Nelder-Mead methods. For the selected application, a Schro¨dinger equation is solved numerically on the second level, 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. The complexity estimates of the computational tasks are model-based, i.e. they use empirical computational data.
Highlights
Current trends in supercomputing show that in order to accumulate high computing power, computers with more, but not faster, processors are used
We propose to control the efficiency of the parallel algorithm on the load balancing stage of the parallelisation template
We introduced a three-level parallelisation template which utilises a new model-based load balancing technique which is based on experimental data
Summary
Current trends in supercomputing show that in order to accumulate high computing power, computers with more, but not faster, processors are used. This trend induces changes in the development of parallel algorithms. The important challenge is to develop parallelisation techniques which enable exploitation of substantially more computational resources than the standard existing methods. This paper deals with problems that can be split into a collection of independent subproblems and this splitting step is repeated iteratively. The solutions of subproblems define the solution of the main problem. An additional parallelization level increases the potential parallelisation degree of a constructed parallel algorithm
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