A three-level parallelisation scheme and application to the Nelder-Mead algorithm

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...

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Bibliographic Details
Published in:Mathematical modelling and analysis Vol. 25; no. 4; pp. 584 - 607
Main Authors: Kriauzienė, Rima, Bugajev, Andrej, Čiegis, Raimondas
Format: Journal Article
Language:English
Published: Vilnius Vilnius Gediminas Technical University 13.10.2020
Subjects:
Algorithms
Linear equations
load balancing and task assignment
Mathematical analysis
Matrices (mathematics)
model-based parallelisation
multi-level parallelisation
Nelder-Mead algorithm
parallel optimisation
Solvers
Task complexity
Wang's algorithm
Nelder-Mead algorithm
model-based parallelisation
multi-level parallelisation
load balancing and task assignment
finite difference methods
Wang's algorithm
parallel optimisation
Schrödinger equation
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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Summary: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. As 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.
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ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2020.12139