A Decomposition of the Tikhonov Regularization Functional Oriented to Exploit Hybrid Multilevel Parallelism

A Decomposition of the Tikhonov Regularization Functional Oriented to Exploit Hybrid Multilevel... We introduce a decomposition of the Tikhonov Regularization (TR) functional which split this operator into several TR functionals, suitably modified in order to enforce the matching of their solutions. As a consequence, instead of solving one problem we can solve several problems reproducing the initial one at smaller dimensions. Such approach leads to a reduction of the time complexity of the resulting algorithm. Since the subproblems are solved in parallel, this decomposition also leads to a reduction of the overall execution time. Main outcome of the decomposition is that the parallel algorithm is oriented to exploit the highest performance of parallel architectures where concurrency is implemented both at the coarsest and finest levels of granularity. Performance analysis is discussed in terms of the algorithm and software scalability. Validation is performed on a reference parallel architecture made of a distributed memory multiprocessor and a Graphic Processing Unit. Results are presented on the Data Assimilation problem, for oceanographic models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Parallel Programming Springer Journals

A Decomposition of the Tikhonov Regularization Functional Oriented to Exploit Hybrid Multilevel Parallelism

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Computer Science; Theory of Computation; Processor Architectures; Software Engineering/Programming and Operating Systems
ISSN
0885-7458
eISSN
1573-7640
D.O.I.
10.1007/s10766-016-0460-3
Publisher site
See Article on Publisher Site

Abstract

We introduce a decomposition of the Tikhonov Regularization (TR) functional which split this operator into several TR functionals, suitably modified in order to enforce the matching of their solutions. As a consequence, instead of solving one problem we can solve several problems reproducing the initial one at smaller dimensions. Such approach leads to a reduction of the time complexity of the resulting algorithm. Since the subproblems are solved in parallel, this decomposition also leads to a reduction of the overall execution time. Main outcome of the decomposition is that the parallel algorithm is oriented to exploit the highest performance of parallel architectures where concurrency is implemented both at the coarsest and finest levels of granularity. Performance analysis is discussed in terms of the algorithm and software scalability. Validation is performed on a reference parallel architecture made of a distributed memory multiprocessor and a Graphic Processing Unit. Results are presented on the Data Assimilation problem, for oceanographic models.

Journal

International Journal of Parallel ProgrammingSpringer Journals

Published: Oct 11, 2016

References

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