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Mathematical Problems in Engineering
Volume 2017, Article ID 2580820, 11 pages
https://doi.org/10.1155/2017/2580820
Research Article

Parallel Multiprojection Preconditioned Methods Based on Subspace Compression

Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, University Campus, Kimmeria, 67100 Xanthi, Greece

Correspondence should be addressed to Christos K. Filelis-Papadopoulos; rg.htud.ee@dapapc

Received 1 February 2017; Revised 5 April 2017; Accepted 11 April 2017; Published 30 July 2017

Academic Editor: Damijan Markovic

Copyright © 2017 Byron E. Moutafis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

During the last decades, the continuous expansion of supercomputing infrastructures necessitates the design of scalable and robust parallel numerical methods for solving large sparse linear systems. A new approach for the additive projection parallel preconditioned iterative method based on semiaggregation and a subspace compression technique, for general sparse linear systems, is presented. The subspace compression technique utilizes a subdomain adjacency matrix and breadth first search to discover and aggregate subdomains to limit the average size of the local linear systems, resulting in reduced memory requirements. The depth of aggregation is controlled by a user defined parameter. The local coefficient matrices use the aggregates computed during the formation of the subdomain adjacency matrix in order to avoid recomputation and improve performance. Moreover, the rows and columns corresponding to the newly formed aggregates are ordered last to further reduce fill-in during the factorization of the local coefficient matrices. Furthermore, the method is based on nonoverlapping domain decomposition in conjunction with algebraic graph partitioning techniques for separating the subdomains. Finally, the applicability and implementation issues are discussed and numerical results along with comparative results are presented.