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dc.contributor.authorLass, Michael
dc.contributor.authorMohr, Stephan
dc.contributor.authorWiebeler, Hendrik
dc.contributor.authorKühne, Thomas D.
dc.contributor.authorPlessl, Christian
dc.contributor.otherBarcelona Supercomputing Center
dc.date.accessioned2018-07-30T08:20:32Z
dc.date.available2018-07-30T08:20:32Z
dc.date.issued2018-07
dc.identifier.citationLass, M. [et al.]. A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices. A: PASC ’18, July 2–4, 2018, Basel, Switzerland. "PASC '18 Proceedings of the Platform for Advanced Scientific Computing Conference". Association for Computing Machinery (ACM), 2018.
dc.identifier.isbn978-1-4503-5891-0
dc.identifier.urihttp://hdl.handle.net/2117/120202
dc.description.abstractWe present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. Following the idea of Approximate Computing, we allow imprecision in the final result in order to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures. We evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution.
dc.description.sponsorshipThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716142) and from the German Research Foundation (DFG) under the project Perfi- cienCC (grant agreement No PL 595/2-1). Compute resources were provided by the Paderborn Center for Parallel Computing (PC 2)
dc.format.extent11 p.
dc.language.isoeng
dc.publisherAssociation for Computing Machinery (ACM)
dc.subjectÀrees temàtiques de la UPC::Informàtica
dc.subject.lcshParallel algorithms
dc.subject.lcshComputational methods in engineering
dc.subject.otherMathematics of computing
dc.subject.otherComputations on matrices
dc.subject.otherTheory of computation
dc.subject.otherNumeric approximation algorithms
dc.subject.otherMassively parallel algorithms
dc.subject.otherDistributed algorithms
dc.subject.otherComputing methodologies
dc.subject.otherMassively parallel algorithms
dc.subject.otherDistributed algorithms
dc.subject.otherApplied computing
dc.titleA Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices
dc.typeConference lecture
dc.subject.lemacAlgorismes paral·lels
dc.subject.lemacSupercomputadors
dc.identifier.doi10.1145/3218176.3218231
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://dl.acm.org/citation.cfm?id=3218231
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/716142/EU/Unravelling the Nature of Green Organic “On-Water” Catalysis via Novel Quantum Chemical Methods/GreenOnWaterCat
local.citation.contributorPASC ’18, July 2–4, 2018, Basel, Switzerland
local.citation.publicationNamePASC '18 Proceedings of the Platform for Advanced Scientific Computing Conference


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