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On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Department of Mathematical Information Technology, University of Jyväskylä.ORCID-id: 0000-0002-3689-0899
Department of Mathematical Information Technology, University of Jyväskylä.
Department of Mathematical Information Technology, University of Jyväskylä; Department of Aeronautics & Astronautics, Stanford University.
2018 (engelsk)Inngår i: Journal of Parallel and Distributed Computing, ISSN 0743-7315, E-ISSN 1096-0848, Vol. 115, s. 56-66Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point performance is analyzed using roofline performance analysis model and the resulting models show that the attained floating point performance is mainly limited by the off-chip memory bandwidth and the effectiveness of a tridiagonal solver used to solve arising tridiagonal subproblems. The performance is accelerated using off-line autotuning techniques.

sted, utgiver, år, opplag, sider
Elsevier, 2018. Vol. 115, s. 56-66
Emneord [en]
Fast direct solver, GPU computing, Partial solution technique, PSCR method, Roofline model, Separable block tridiagonal linear system
HSV kategori
Forskningsprogram
administrativ databehandling
Identifikatorer
URN: urn:nbn:se:umu:diva-145462DOI: 10.1016/j.jpdc.2018.01.004ISI: 000427809200005OAI: oai:DiVA.org:umu-145462DiVA, id: diva2:1187714
Tilgjengelig fra: 2018-03-05 Laget: 2018-03-05 Sist oppdatert: 2018-06-09bibliografisk kontrollert

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