Parallel alternating iterative algorithms with and without overlapping on multicore architectures. (November 2016)

• Record Type: Journal Article
• Authors: Migallón, Héctor; Migallón, Violeta; Penadés, José
• Is Part Of: Advances in engineering software. Volume 101(2016)
• Page Start: 27
• Page End: 36
• Publication Date: 2016-11
• Subjects: Block two-stage methods -- Alternating iterations -- Overlapping -- Parallel computing -- Shared memory -- Distributed memory -- Laplace's equation -- Markov chains; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2015.10.012
• Languages: English
• ISSNs: 0965-9978

Abstract

Abstract: We consider the problem of solving large sparse linear systems where the coefficient matrix is possibly singular but the equations are consistent. Block two-stage methods in which the inner iterations are performed using alternating methods are studied. These methods are ideal for parallel processing and provide a very general setting to study parallel block methods including overlapping. Convergence properties of these methods are established when the matrix in question is either M -matrix or symmetric matrix. Different parallel versions of these methods and implementation strategies, with and without overlapping blocks, are explored. The reported experiments show the behavior and effectiveness of the designed parallel algorithms by exploiting the benefits of shared memory inside the nodes of current SMP supercomputers.